ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2

Choose the correct answer from the given four options (1-2):
Question 1.
If 295×703 is divisible by 11, then value of x is
(a) 5
(b) 6
(c) 7
(d) 8
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 1

Question 2.
If C.P. of an article is ₹500 and S.P. is ₹600, then, his profit % is
(a) 10%
(b) 15%
(c) 20%
(d) 25%
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 2

Question 3.
Find the values of the letters in the following and give reasons for the steps involved:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 3
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 4

Question 4.
Ramu bought a fan for ₹1080 including 8% VAT. Find the price of fan before VAT was added.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 5

Question 5.
Find the amount and compound interest on ₹2000 for 2 years at 5% per annum, interest payable yearly.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 6

Question 6.
If P = {letters of the word HYDERABAD} and Q= {letters ofthewordALLAHABAD}, find
(i) P ∪ Q
(ii) P ∩ Q
Also verify that
n(P ∪ Q) = n(P) + n(Q) – n(P ∩ Q).
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 7

Question 7.
A blanket was marked for ₹500. A shopkeeper allows a discount of 10%. But due to partial damage in the blanket he has to give an extra discount of 20%. Find the S.P. of the blanket.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 8

Question 8.
In a 3 digit number unit’s digit, ten’s digit and hundred’s digit are in the ratio 3 : 5 : 7. If the difference of original number and number obtained by reversing the digits is 396, find the number.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 9

Question 9.
In an exam atleast 40% marks are required to pass the exam. Rohit uses unfair means to pass the exam but fails by 20 marks. If he scored 220 marks, then find the maximum marks.
Is using unfair means in exam is good? Why should we not use unfair means?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 10

Question 10.
Find the sum invested for \(1 \frac{1}{2}\) years compounded half-yearly at the rate of 8% p.a. that will amount to ₹ 17576.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 2 11

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1

ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1

Choose the correct answer from the given four options (1-2):
Question 1.
Sum of rational number \(\frac { 5 }{ 7 }\) and its additiveinverse is
(a) 1
(b) 0
(c) -1
(d) none of these
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 1

Question 2.
Product of two rational numbers is 1. If one of them is \(\frac { 4 }{ 5 }\), then other is
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 2
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 3

Question 3.
Find the value of x for which \(\left(\frac{4}{9}\right)^{x} \times\left(\frac{3}{2}\right)^{-1}\) = \(\frac{8}{27}\).
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 4

Question 4.
Express the following numbers in standard form:
(i) 0.0000000000578
(ii) 345700000000000
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 5

Question 5.
Insert ten rational numbers between \(\frac{-4}{5}\) and \(\frac{2}{3}\).
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 6

Question 6.
Find the cube root of 50653.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 7

Question 7.
Find the smallest number by which 3645 should be divided so that quotient is a perfect cube.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 8

Question 8.
If p = \(\frac{-3}{5}\), q = \(\frac{1}{2}\), r= \(\frac{-7}{9}\),then verify p × (q + r) = p × q + p × r.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 9
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 10

Question 9.
Find the square root of 7056 by prime factorisation method.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 11

Question 10.
Find the least number which must be added to 59000 to make it a perfect square.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Model Question Paper 1 12

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress

Question 1.
Each student from the group of 40 students was asked to roll a dice independently. The results are given below:
2, 3, 3, 4, 1, 5, 2, 6, 1, 4, 2, 3, 4, 4, 6, 1, 5, 5, 2, 4, 5, 5, 3, 1, 6, 5, 4, 2, 3, 6, 1, 1, 4, 4, 5, 3, 2, 2, 6,6
Make a frequency distribution table for the same.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 1

Question 2.
The marks obtained by 30 students of a class in a test of maximum marks 20 are as follows:
15, 11, 12, 10, 9, 8, 19, 13, 16, 3, 2, 17, 18, 19, 14, 6, 20, 15, 16, 12, 10, 4, 9, 8, 12, 17, 18, 20, 19, 12.
Prepare a frequency distribution table for the above data using class intervals 0-4, 4-8 and so on.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 2

Question 3.
Construct a frequency distribution table for the following weights (in grams) of 35 oranges, using class intervals 40—45, 45-50 and so on.
30, 40, 45, 32, 43, 50, 55, 63, 72, 73, 62, 61, 54, 53, 50, 43, 76, 38, 54, 55, 66, 70, 74, 75, 45, 47, 59, 58, 60, 63, 74, 33, 35, 70, 68.
(i) How many classes are there in the frequency distribution table?
(ii) Which weight group has the lowest frequency?
(iii) Which weight group has the highest frequency?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 3

Question 4.
Draw a histogram of the following data:
Marks obtained by students in a Mathematics Paper of maximum marks 100.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 4
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 5
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 6

Question 5.
The following data represents the number of students using a different mode of transportation to come to school.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 7
Draw a pie chart to represent this data Pie chart is given below:
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 8
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 9

Question 6.
Answer the following questions based on the pie chart given below:
(i) Which type of programmes are viewed the most?
(ii) Which type of programmes are viewed the least?
(iii) Which two types of programmes have number of viewers equal to those watching sports channels?
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 10
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 11

Question 7.
Suppose you spin the wheel shown in adjoining figure.
(i) List the outcomes of getting a green sector and not getting a green sector on this wheel.
(ii) Find the probability of getting a green sector.
(iii) Find the probability of not getting a green sector.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 12
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 13

Question 8.
A bag has 4 red and 2 yellow balls. A ball is drawn from the bag without looking into the bag. What is the probability of getting
(i) a red ball?
(ii) not a red ball?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 14

Question 9.
Three coins are tossed together, find the probability of getting
(i) atmost 2 heads
(ii) 3 heads.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 15

Question 10.
A letter is chosen from the word ‘RECTANGLE’. What is the probability that it is
(i) a consonant
(ii) not a consonant.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Check Your Progress 16

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) Bar graphs are ……….. representation of ungrouped data.
(ii) In a grouped frequency distribution, the difference between lower limit and upper limit of a class is called ………..
(iii) The mid point of the class interval is called ………..
(iv) Bar graphs of grouped data are called ………..
(v) The circle graphs are commonly called ………..
(vi) An experiment which has more than one possible outcomes and it is not possible to predict the outcome in advance is called ………..
(vii) The outcomes which ensures the occurrence of an event are called ………..
(viii) An event which never happens is called ………..
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 1

Question 2.
State whether the following statements are true (T) or false (F):
(i) The data arranged in ascending or descending order of size is called data array.
(ii) The lower limit of class 10-20 is 20.
(iii) The class size of class 20-30 is 10.
(iv) The class mark of 25-35 is 30.
(v) There is no difference between bar graphs and histograms.
(vi) In histograms the breadth of a rectangle is meaningless.
(vii) In histograms, there is no gap between two adjacent rectangle.
(viii) In a pie chart, size of each sector is proportional to the value of item represented by it.
(ix) In a pie chaiangle of sector
= \(\frac{\text { value of item }}{\text { sum of values of all items }} \times 180^{\circ}\)
(x) In tossing a coin getting head or tail are equally likely events.
(xi) Probability of an event E satisfies 0 ≤ P(E) ≤ 1.
(xii) P(occurrence of an event) = P(non occurence of an event).
(xiii) Total number of outcomes when two dice are rolled togehter = 6 + 6.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 3

Multiple Choice Questions
Study the following frequency distribution table:
The table shows the pocket money (in ?) per month of 50 students. Choose the correct answer from the given four options for questions 3 to 7;
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 4

Question 3.
Size of the class-intervals is
(a) 50
(b) 20
(c) 10
(d) 30
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 5

Question 4.
The class having the maximum frequency is
(a) 10-20
(b) 20-30
(c) 30-40
(d) 40-50
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 6

Question 5.
The upper limit of the class having minimum frequency is
(a) 30
(b) 40
(c) 50
(d) 60
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 7

Question 6.
Which two are classes having the same frequency?
(a) 10-20 and 20-30
(b) 20-30 and 30-40
(c) 30-40 and 50-60
(d) 40-50 and 50-60
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 8

Question 7.
The frequency of class whose class mark is 25 is
(a) 14
(b) 11
(c) 10
(d) 4
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 9

The pie graph shown in the adjoining figure representing the different subjects liked by the students of class VIII. Study the pie graph carefully and choose the correct answer from the given four options for questions 8 to 11.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 10

Question 8.
Which subject is liked by the maximum number of students
(a) Maths
(b) Science
(c) S. Science
(d) English
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 11

Question 9.
Which subject is liked by the minimum number of students
(a) Maths
(b) Science
(c) S. Science
(d) English
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 12

Question 10.
If there are 200 students in class VIII then the number of students who like S. Science
(a) 10
(b) 20
(c) 40
(d) 80
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 13

Question 11.
Number of students who like Science
(a) 20
(b) 40
(c) 60
(d) 80
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 14

Choose the correct answer from the given four options (12 to 17):
Question 12.
Probability of getting the sum as 4 when a pair of dice is rolled
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 15
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 16

Question 13.
Probability of getting exactly 2 heads when three coins are tossed together
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 17
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 18

Question 14.
Probability of selecting a consonant from the letters of the word ‘FATHER’
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 19
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 20

Question 15.
Probability of getting more than 2 heads when a pair of coins is tossed.
(a) 1
(b) \(\frac{1}{2}\)
(c) \(\frac{1}{3}\)
(d) 0
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 21

Question 16.
Probability of getting a red ball from a bag containing 20 red balls
(a) 0
(b) 1
(c) \(\frac{1}{20}\)
(d) \(\frac{1}{2}\)
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 22

Question 17.
Probability of getting a non-red ball from a bag containing 4 red, 5 blue and 3 black balls is
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 23
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 24

Value Based Questions
Question 1.
Draw a pie chart of the data given below:
The time spent by a Class VIII student during a day.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 25
Should a student of class VIII study for just 2 hours daily? Which time is considered the best time for self-study?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 26
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 27

Question 2.
From a bag containing 2 saffron, 3 white and 4 green balls a ball is drawn at random. Find the probability that ball drawn is
(i) Saffron
(ii) White
(iii) Green
Which are three colours in our National Flag? What values did they indicate? What values are being promoted?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 28

Question 3.
Four defective oranges are accidentally mixed with 16 good ones. One orange is drawn at random. Find the probability that the orange drawn is good one.
What will happen if 4 bad persons are mixed with 16 good ones?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 29

Higher Order Thinking Skills (Hots)
Question 1.
A bag contains 12 balls out of which x are black.
(i) If a ball drawn at random, what is the probability that it will be a black ball?
(ii) If 6 more black balls are put in the bag, the probability of drawing a black ball will be double than that of (i). Find the value of x.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 30

Question 2.
Ankita and Nagma are friends. They were both born in 1998. What is the probability that they have
(i) same birthday?
(ii) different birthday?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Objective Type Questions 31

ML Aggarwal Class 8 Solutions for ICSE Maths

CBSE Sample Papers for Class 10 Maths Paper 2

CBSE Sample Papers for Class 10 Maths Paper 2 is part of CBSE Sample Papers for Class 10 Maths Here we have given CBSE Sample Papers for Class 10 Maths Paper 2 According to new CBSE Exam Pattern, MCQ Questions for Class 10 Maths Carries 20 Marks.

CBSE Sample Papers for Class 10 Maths Paper 2

Board CBSE
Class X
Subject Maths
Sample Paper Set Paper 2
Category CBSE Sample Papers

Students who are going to appear for CBSE Class 10 Examinations are advised to practice the CBSE sample papers given here which is designed as per the latest Syllabus and marking scheme as prescribed by the CBSE is given here. Paper 2 of Solved CBSE Sample Papers for Class 10 Maths is given below with free PDF download solutions.

Time: 3 Hours
Maximum Marks: 80

GENERAL INSTRUCTIONS:

  • All questions are compulsory.
  • This question paper consists of 30 questions divided into four sections A, B, C and D.
  • Section A comprises of 6 questions of 1 mark each, Section B comprises of 6 questions of 2 marks each, Section C comprises of 10 questions of 3 marks each and Section D comprises of 8 questions 1 of 4 marks each.
  • There is no overall choice. However, internal choice has been provided in one question of 2 marks, 1 three questions of 3 marks each and two questions of 4 marks each. You have to attempt only one of the alternatives in all such questions.
  • In question of construction, drawings shall be neat and exactly as per the given measurements.
  • Use of calculators is not permitted. However, you may ask for mathematical tables.

SECTION A

Question numbers 1 to 6 carry 1 mark each.

Question 1.
Find the value of k for which the following pair of linear equations has a unique solution:
2x + 3y = 7; (k – 1)x + (k + 2)y = 3k.

Question 2.
Find the nature of the roots of quadratic equation 2x² – √5 x + 1 = 0.

Question 3.
What is the probability that a non-leap year has 53 Mondays?

Question 4.
A die is thrown once. Find the probability of getting a prime number.

Question 5.
Find the mode of the data, whose mean and median are given by 10.5 and 11.5 respectively.

Question 6.
In the adjoining figure, DE || BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, find the value of x.
CBSE Sample Papers for Class 10 Maths Paper 2 6

SECTION B

Question numbers 7 to 12 carry 2 marks each.

Question 7.
Find HCF and LCM of 90 and 144 by method of prime factorisation.

Question 8.
Find the values of a and b for which the following pair of linear equations has infinitely many solutions:
3x – (a + 1)y = 2b – 1; 5x + (1 – 2a)y = 3b.

Question 9.
Without using trigonometric tables, evaluate the following:
(cos² 25° + cos² 65°) + cosec θ . sec (90° – θ) – cot θ tan (90° – θ).

Question 10.
ABC is a triangle and G (4, 3) is the centroid of the triangle. If A, B and C are the points (1, 3), (4, b) and (a, 1) respectively, find the values of a and b. Also find the length of side BC.

Question 11.
In the adjoining figure, DE || AC and \(\frac { BE }{ EC } =\frac { BC }{ CP } \) . Prove that DC || AP.
CBSE Sample Papers for Class 10 Maths Paper 2 11

Question 12.
In the adjoining figure, a circle is inscribed in a quadrilateral ABCD in which ∠B = 90°. If AD = 23 cm, AB = 29 cm and DS = 5 cm, find the radius (r) of the circle.
CBSE Sample Papers for Class 10 Maths Paper 2 12

SECTION C

Question numbers 13 to 22 carry 3 marks each.

Question 13.
If two zeroes of the polynomial x4 + 3x3 – 20x2 – 6x + 36 are √2 and – √2 , find the other zeroes of the polynomial.

Question 14.
If α and β are zeroes of the polynomial 6x² – 7x – 3, then form a quadratic polynomial whose zeroes are \(\frac { 1 }{ \alpha } \) and \(\frac { 1 }{ \beta } \).

Question 15.
How many terms of the A.P. -6, \(\frac { 11 }{ 2 }\), -5,……. double answer.are needed to give the sum – 25? Explain the
OR
The 19th term of an AP is equal to three times its 6th term. If its 9th term is 19, find the AP.

Question 16.
The father’s present age is six times his son’s ages. Four years hence the age of the father will be four times his son’s age. Find the present ages of the father and son.
OR
The ratio of incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save Rs 2000 per month, find their monthly incomes.

Question 17.
ABC is a right triangle, right angled at C. If p is the length of perpendicular from C to AB and a, b, c have usual meanings, then prove that \(\frac { 1 }{ { p }^{ 2 } } =\frac { 1 }{ { a }^{ 2 } } +\frac { 1 }{ { b }^{ 2 } } \)
OR
If the diagonals of a quadrilateral divide each other proportionally, prove that it is a trapezium.

Question 18.
PQ is a tangent to a circle with centre O at the point Q: A chord QA is ‘drawn parallel to PO. If AOB is a diameter of the circle, prove that PB is tangent to the circle at the point B.

Question 19.
The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14 cm). If the volume of bucket is 5390 cm3, then find the value of r.

Question 20.
Find the area of the major segment APB in adjoining figure, of a circle of radius 35 cm and ∠AOB = 90°.
CBSE Sample Papers for Class 10 Maths Paper 2 20
OR
In adjoining figure, a semicircle is drawn with O as centre and AB as diameter. Semicircles are drawn with AO and OB as diameters. If AB = 28 m, find the perimeter of the shaded region.
CBSE Sample Papers for Class 10 Maths Paper 2 20.1

Question 21.
Prove that :
CBSE Sample Papers for Class 10 Maths Paper 2 21

Question 22.
Prove that :
CBSE Sample Papers for Class 10 Maths Paper 2 22

SECTION D

Question numbers 23 to 30 carry 4 marks each.

Question 23.
Prove that √5 is an irrational number and hence show that 2 + √5 is also an irrational number.

Question 24.
If two vertices of an equilateral triangle are (3, 0) and (6, 0), find the third vertex.
OR
The mid-points D, E and F of the sides AB, BC and CA of a triangle are (3, 4), (8, 9) and (6, 7) respectively. Find the coordinates of the vertices of the triangle.

Question 25.
Water is flowing at the rate of 15 km/hour through a pipe of diameter 14 cm into a cuboidal pond which is 50 m long and 44 m wide. In what time will the level of water in the pond rise by 21 cm?

Question 26.
While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalise the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away in time, the pilot increased the speed by 100 km/h. Find the original speed/hour of the plane.
Do you appreciate the values shown by pilot, namely promptness in providing help to the injured and his efforts to reach in time.

Question 27.
Draw a pair of tangents to a circle of radius 3 cm which are inclined at an angle of 60° to each other.

Question 28.
The angle of elevation of the top of a building from the foot of a tower is 30° aid the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 50 m high, find the height of the building.
OR
The angles of depression of two ships from the top of a lighthouse and on the same side of it are found to be 45° and 30°. If the ships are 200 m apart, find the height of the lighthouse.

Question 29.
Three coins are tossed simultaneously, find the probability of getting:
(i) atleast one head
(ii) atmost two heads
(iii) exactly 2 heads
(iv) no head.

Question 30.
The mean of the following frequency distribution is 62.8 and the sum Of all the frequencies is 50. Compute the missing frequencies f1 and f2:
CBSE Sample Papers for Class 10 Maths Paper 2 30
OR
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mode and mean of the data:
CBSE Sample Papers for Class 10 Maths Paper 2 30.1

Answers

Answer 1.
For unique solution, \(\frac { 2 }{ k-1 } \neq \frac { 3 }{ k+2 } \) ⇒ 2k + 4 ≠ 3k – 3
⇒ k ≠ 7
Hence, the given pair of linear equations will have unique solution for all real values of k except 7.

Answer 2.
Given 2x² – √5x + 1 = 0
D = (-√5)² – 4 x 2 x 1 = 5 – 8 = – 3
∵D < 0, therefore, given equation has no real roots.

Answer 3.
There are 365 days in a non-leap year.
365 days = 52 weeks + 1 day
∴ One day can be M, T, W, Th, F, S, Su = 7 ways
∴ P(53 Mondays in non-leap year) = \(\frac { 1 }{ 7 }\)

Answer 4.
Total number of outcomes = 6(1, 2, 3, 4, 5 or 6)
Favourable number of outcomes = 3(2, 3, 5)
∴ P(prime number) = \(\frac { 3 }{ 6 } =\frac { 1 }{ 2 } \)

Answer 5.
Mode = 3 Median – 2 Mean .
= 3 x 11.5 – 2 x 10.5 = 34.5 – 21 – 13.5
Hence, mode = 13.5

Answer 6.
∵ DE || BC
∴ By Basic Proportionality Theorem, we have
CBSE Sample Papers for Class 10 Maths Paper 2 6
\(\frac { AD }{ DB } =\frac { AE }{ EC } \)
⇒ \(\frac { x }{ x-2 } =\frac { x+2 }{ x-1 } \)
⇒ x (x – 1) = (x – 2) (x + 2)
⇒ x² – x – x² – 4
⇒ -x = -4
⇒ x = 4.

Answer 7.
90 = 2 x 3 x 3 x 5
and 144 = 2 x 2 x 2 x 2 x 3 x 3
∴ HCF = 2 x 3 x 3 = 18
and LCM = 2 x 2 x 2 x 2 x 3 x 3 x 5 = 720
Hence, HCF = 18 and LCM = 720.

Answer 8.
Given 3x – (a + 1 )y – (2b – 1) = 0
and 5x + (1 – 2a)y – 3b = 0
CBSE Sample Papers for Class 10 Maths Paper 2 8
Hence, a = 8 and b = 5.

Answer 9.
(cos² 25° + cos² 65°) + cosec θ . sec (90° – θ) – cot θ . tan (90° – θ)
= cos² 25° + cos² (90° – 25°) + cosec θ . cosec θ – cot θ . cot θ
= cos² 25° + sin² 25° + cosec² θ – cot² θ
= 1 + 1
= 2.

Answer 10.
Since G (4, 3) is the centroid of ∆ABC, we have
CBSE Sample Papers for Class 10 Maths Paper 2 10

Answer 11.
In ∆ABC, DE || AC
CBSE Sample Papers for Class 10 Maths Paper 2 11

Answer 12.
AR = AQ, DR = DS, BP = BQ (lengths of tangents)
but DS = 5 cm => DR = 5 cm.
AR = AD – DR = 23 cm – 5 cm = 18 cm => AQ = 18 cm.
BQ = AB – AQ = 29 cm – 18 cm = 11 cm.
As AB is tangent to the circle at Q, OQ ⊥ AB
=> ∠OQB = 90°.
Also ∠B = 90° (given) => OQBP is a rectangle.
But BP = BQ => OQBP is a square.
∴ Radius = r = OQ = BQ = 11 cm.
CBSE Sample Papers for Class 10 Maths Paper 2 12

Answer 13.
∴ √2 and -√2 are the zero’s of the given polynomial.
∴ (x – √2) (x + √2) i.e. (x² – 2) is a factor of the given polynomial.
CBSE Sample Papers for Class 10 Maths Paper 2 13
To find the other two zero’s, we proceed as follows:
x² + 3x – 18 = 0
⇒ (x + 6) (x – 3) = 0
⇒ x + 6 = 0 or x – 3 = 0
⇒ x = -6 or x = 3
Hence, other zero’s are -6 and 3.

Answer 14.
Given α and β are zero’s of quadratic polynomial 6x² – 7x – 3,
CBSE Sample Papers for Class 10 Maths Paper 2 14

Answer 15.
Here, a = -6, d = \(-\frac { 11 }{ 2 }- (-6)\) = \(-\frac { 11 }{ 2 }+6\) = \(\frac { 1 }{ 2 }\) ,Sn = -25.
We are required to find n.
CBSE Sample Papers for Class 10 Maths Paper 2 15
CBSE Sample Papers for Class 10 Maths Paper 2 15.1

Answer 16.
Let the father’s present age be x years
and the son’s present age be y years.
According to given, x – 6y …(i)
4 years later,
father’s age = (x + 4) years
and son’s age = (y + 4) years
∴ (x + 4) = 4(y + 4)
=> x – 4y = 12 …(ii)
Putting the value of x from (i) in (ii), we get
6y – 4 y = 12 => 2y = 12 => y = 6
∴ x = 6 x 6 = 36
Hence, father’s present age = 36 years and son’s present age = 6 years
OR
Let the incomes per month of two persons be Rs x and Rs y respectively. As each person saves Rs 2000 per month, so their expenditures are Rs (x – 2000) and Rs (y – 2000) respectively.
According to given, we have
\(\frac { x }{ y } =\frac { 9 }{ 7 } \) i.e- 7x – 9y = 0 …(i)
and \(\frac { x-2000 }{ y-2000 } =\frac { 4 }{ 3 } \) i.e. 3x – 4y + 2000 = 0 …(ii)
Multiplying equation (i) by 3 and equation (ii) by 7, we get
21x – 27y = 0 …(iii) and 21x – 28y + 14000 = 0 …(iv)
Subtracting equation (iv) from equation (iii), we get
y – 14000 = 0 => y = 14000.
Substituting this value of y in (i), we get
7x – 9 x 14000 = 0 =>x = 18000.
Hence, the monthly incomes of the two persons are Rs 18000 and Rs 14000 respectively.

Answer 17.
In ∆ACB and ∆CDB,
∠ACB = ∠CDB (both 90°)
∠B = ∠B (common)
∴ ∆ACB ~ ∆CDB (by AA similarity criterion)
CBSE Sample Papers for Class 10 Maths Paper 2 17
CBSE Sample Papers for Class 10 Maths Paper 2 17.1

Answer 18.
Given a circle with centre O and PQ is tangent to the circle at the point Q from an external point P. Chord QA is parallel to PO and AOB is a diameter.
We need to prove that PB is tangent to the circle at the point B.
Join OQ and mark the angles as shown in the adjoining figure.
CBSE Sample Papers for Class 10 Maths Paper 2 18
As QA || PO,
∠1 = ∠2 (alt. ∠s)
and ∠4 = ∠3 (corres. ∠s)
.But ∠2 = ∠3 (∵ in ∆OAQ, OA = OQ being radii)
∴ ∠1 = ∠4.
In ∆OPB and ∆OPQ,
OB = OQ (radii of same circle)
∠1 = ∠4 (proved above)
OP = OP (common)
∴ ∆OPB ≅ ∆OPQ (SAS congruence rule)
∴ ∠OBP = ∠OQP (c.p.c.t)
=> ∠OBP = 90° (tangent is ⊥ to radius ,OQ⊥PQ)
=> OB ⊥ PB i.e. radius is perpendicular to PB at point B.
Therefore, PB is tangent to the circle at the point B.

Answer 19.
Given h = 15 cm, R = 14 cm, ‘r’ = r cm and volume of bucket = 5390 cm³
∵Volume of bucket = volume of frustum of cone
CBSE Sample Papers for Class 10 Maths Paper 2 19
∴r cannot be negative
∵Radius = r = 7 cm.

Answer 20.
Given r = 35 cm and ∠AOB = 90°
Area of minor segment = area of minor sector – area (∆OAB)
CBSE Sample Papers for Class 10 Maths Paper 2 20

Answer 21.
CBSE Sample Papers for Class 10 Maths Paper 2 21

Answer 22.
CBSE Sample Papers for Class 10 Maths Paper 2 22

Answer 23.
Let √5 be a rational number, then
√5 = \(\frac { p }{ q }\), where p, q are integers, q ≠ 0 and p, q have no common factors (except 1)
=>\(5=\frac { { p }^{ 2 } }{ { q }^{ 2 } } \) => p² = 5q²
As 5 divides 5q², so 5 divides p², but 5 is prime.
=> 5 divides p
Let p = 5m, where m is an integer.
Substituting this value of p in (i), we get
(5m)² = 5q² => 25m² = 5q² => 5m² = q²
As 5 divides 5m², so 5 divides q², but 5 is prime
=> 5 divides q
Thus p and q have a common factor 5. This contradicts that p and q have no common factors (except 1)
Hence, √5 is not a rational number.
So, we conclude that √5 is an irrational number.
Let 2 + √5 be a rational number, say r
Then, 2 + √5 = r => √5 = r – 2
As r is rational, r – 2 is rational => √5 is rational
But this contradicts the fact that √5 is irrational.
Hence, our assumption is wrong. Therefore, 2 + √5 is an irrational number.

Answer 24.
Given vertices are A(3, 0) and B(6, 0) and let third vertex be C(x, y), then
CBSE Sample Papers for Class 10 Maths Paper 2 24
OR
Let the vertices A, B and C of the triangle ABC be (x1 y1), (x2, y2) and (x3 y3) respectively.
Since points D and F are mid-points of the sides AB and
AC respectively, by mid-point theorem, DF || BC and
DF = \(\frac { 1 }{ 2 }BC\) but E is mid-point of BC, so DF || BE and
DF = BE.
Therefore, DBEF is a parallelogram.
Similarly, DECF and DEFA are parallelograms.
Since the diagonals of a parallelogram bisect each other, mid-points of diagonals BF and DE are same.
CBSE Sample Papers for Class 10 Maths Paper 2 24.1
CBSE Sample Papers for Class 10 Maths Paper 2 24.2
CBSE Sample Papers for Class 10 Maths Paper 2 24.3

Answer 25.
Radius of pipe = \(\frac { 14 }{ 2 }\) cm = 7 cm = \(\frac { 7 }{ 100 }\) m = 0.07 m
As the water is flowing at the rate of 15 km per hour,
the length of water delivered by the circular pipe in 1 hour
= 15 km = 15000 m
Volume of water delivered by the circular pipe in 1 hour
CBSE Sample Papers for Class 10 Maths Paper 2 25
Hence, the level of water in the pond rise by 21 cm in 2 hours.

Answer 26.
Let the original speed of the aeroplane be x km/h.
Time taken to cover the distance of 1500 km = \(\frac { 1500 }{ x }\) hours
New speed of the aeroplane = (x + 100) km/h.
Time taken to cover the distance of 1500 km at new speed = \(\frac { 1500 }{ x+100 }\) hours
CBSE Sample Papers for Class 10 Maths Paper 2 26
=> x² + 100x – 300000 = 0
=> x² + 600x – 500x – 300000 = 0 => (x – 500) (x + 600) = 0
=> x = 500 or x = -600
But speed cannot be negative.
Hence, the original speed of the aeroplane = 500 km/h.
Yes, I appreciate the values shown by the pilot. Along with showing concern for the injured passenger he did not fail to perform his duty, by increasing the speed of the plane, he reached the destination on time.

Answer 27.
Steps of construction:
1. Draw a circle of radius 3 cm with O as its centre.
2. Draw any radius OA.
3. At O, construct ∠AOC = 120° to meet the circle at B.
4. At A, construct ∠OAR = 90°.
5. At B, construct ∠OBQ = 90° to meet AR at P.
CBSE Sample Papers for Class 10 Maths Paper 2 27
Then PA and PB are tangents to the circle inclined at an angle of 60° to each other.
Justification:
As ∠APB and ∠AOB are supplementary, so ∠APB = 60°.

Answer 28.
Let CD = h metres be the height of the building and AB be the tower, then AB = 50 m.
Let BD = d metres be the distance between the foot of the tower and the foot of the building.
Given, ∠CBD = 30° and ∠ADB = 60°.
From right angled ∆CBD, we get
CBSE Sample Papers for Class 10 Maths Paper 2 28
OR
Let the height of the lighthouse AB be h metres and C, D be the positions of two ships. The angles of depressions are shown in the adjoining figure.
Then ∠ACB = 45° and ∠ADB = 30°
Given CD = 200 m, let BC = x metres.
From right angled ∆ABC, we get
CBSE Sample Papers for Class 10 Maths Paper 2 28.1
CBSE Sample Papers for Class 10 Maths Paper 2 28.2
CBSE Sample Papers for Class 10 Maths Paper 2 28.3

Answer 29.
When three coins are tossed simultaneously, the outcomes of the random experiment are:
HHH, HHT, HTH, THH, HTT, THT, TTH, TIT
It has 8 equally likely outcomes.
(i) The outcomes favourable to the event ‘atleast one head’ are
HHH, HHT, HTH, THH, HTT, THT, TTH; which are 7 in number.
∴ P(atleast one head) = \(\frac { 7 }{ 8 }\)
(ii) The outcomes favourable to the event ‘atmost two heads’ are
HHT, HTH, THH, THT, HTT, TTH, TTT; which are 7 in number.
∴P(atmost two heads) = \(\frac { 7 }{ 8 }\)
(iii) The outcomes favourable to the event ‘exactly 2 heads’ are
HHT, HTH, THH; which are 3 in number.
∴ P(exactly two heads) = \(\frac { 3 }{ 8 }\)
(iv) The only outcome favourable to the event ‘no head’ is TTT.
∴P(no head) = \(\frac { 1 }{ 8 }\)

Answer 30.
Given, sum of all frequencies = 50
CBSE Sample Papers for Class 10 Maths Paper 2 30
CBSE Sample Papers for Class 10 Maths Paper 2 30.1

We hope the CBSE Sample Papers for Class 10 Maths Paper 2 help you. If you have any query regarding CBSE Sample Papers for Class 10 Maths Paper 2, drop a comment below and we will get back to you at the earliest.

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3

Question 1.
List the outcomes you can see in these experiments.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 1
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 2

Question 2.
A die is rolled once. Find the probability of getting
(i) an even number
(ii) a multiple of 3
(iii) not a multiple of 3
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 3

Question 3.
Two coins are tossed together. Find the probability of getting
(i) two tails
(ii) atleast one tail
(iii) no tail
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 4

Question 4.
Three coins are tossed together. Find the probability of getting
(i) atleast two heads
(ii) atleast one tail
(iii) atmost one tail.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 5

Question 5.
Two dice are rolled simultaneously. Find the probability of getting
(i) the sum as 7
(ii) the sum as 3 or 4
(iii) prime numbers on both the dice.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 6

Question 6.
A fcox contains 600 screws, one tenth are rusted. One screw is taken out at random from the box. Find the probability that it is
(i) a rusted screw
(ii) not a rusted screw
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 7

Question 7.
A letter is chosen from the word ‘TRIANGLE’. What is the probability that it is a vowel?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 8

Question 8.
A bag contains 5 red, 6 black and 4 white balls. A ball is drawn at random from the bag, find the probability the ball is drawn is
(i) white
(ii) not black
(iii) red or black
(iv) neither red nor black
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 9

Question 9.
A box contains 17 cards numbered 1, 2, 3, ……….,17 and are mixed thoroughly. A card is drawn at random from the box. Find the probability that the number on the card is
(i) odd
(ii) even
(iii) prime
(iv) divisible by 3
(v) divisible by 2 and 3 both
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 10

Question 10.
A card is drawn from a well-shuffled pack of 52 cards. Find the probability that the card drawn is:
(i) an ace
(ii) a red card
(iii) neither a king nor a queen
(iv) a red face card or an ace
(v) a card of spade
(vi) non-face card of red colour.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 11

Question 11.
In a lottery, there are 5 prized tickets and 995 blank tickets. A person buys a lottery ticket. Find the probability of his winning a prize.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.3 12

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2

Question 1.
The following data represents the different number of animals in a zoo. Prepare a pie chart for the given data.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 1
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 3

Question 2.
The following data represents the monthly expenditure of a family (in T) on various items. Draw a pie chart to represent this data.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 4
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 5
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 6

Question 3.
The following data represents the percentage distribution of the expenditure incurred in publishing a book.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 7
Draw a pie chart to represent this data.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 8
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 9

Question 4.
The following data represents the number of students got admission in different streams of a college:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 10
Draw a pie chart to represent this data.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 11
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 12

Question 5.
The adjoining pie chart shows the expenditure of a country on various sports during year 2012. Study the pie chart carefully and answer the following questions:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 13
(i) What percent of total expenditure is spent on cricket?
(ii) How much percent more is spent on hockey than that on tennis?
(iii) If the total amount spent on sports in 2012 is ₹1,80,00,000, then find amount spent on Badminton,
(iv) If the total amount spent on sports in 2012 is ₹2,40,00,000 then find the amount spent on cricket and hockey together.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 14

Question 6.
The adjoining pie chart shows the number of students enrolled in class VI to class X of a school.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 15
If 1440 students are enrolled from VI to X, then answer the following questions:
(i) How many students are enrolled in class VIII?
(ii) How many students are more in class IX than in class X?
(iii) What is the sum of students enrolled in VII and VIII?
(iv) Find the ratio of students enrolled in VI to students enrolled in X.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.2 16

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1

Question 1.
The result of a survey of 200 people about their favourite fruit is given below:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 1
Represent the above data by a bar graph.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 2
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 3

Question 2.
Mr Khurana has two kitchen appliance stores. He compares the sales of two stores during a month and recovered as given below:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 4
Represent the above data by a double bar graph.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 5
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 6

Question 3.
The number of goals scored by a football team in different matches is given below:
3, 1, 0, 4, 6, 0, 0, 1, 1, 2, 2, 3, 5, 1, 2, 0, 1, 0, 2, 3, 9, 2, 0, 1, 0, 1, 4, 1, 0, 2, 5, 1, 2, 2, 3, 1, 0, 0, 0, 1, 1, 0, 2, 3, 0, 1, 5, 2, 0
Make a frequency distribution table using tally marks.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 7

Question 4.
Given below a bar graph:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 8
Read the bar graph carefully and answer the following questions:
(i) What is the information given by the bar graph?
(ii) On which item the expenditure is maximum?
(iii) On which item the expenditure is minimum?
(iv) State whether true or false:
Expenditure on education is twice the expenditure on clothing.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 9

Question 5.
Given below a double bar graph.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 10
Read the double bar graph carefully and answer the following questions:
(i) What is the information given by the double graph?
(ii) Which mode of transport girls using more than the boys?
(iii) Which mode of transport boys using the most?
(iv) In which mode of transport number of girls is half the number of boys?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 11

Question 6.
Using class intervals 0-5, 5-10, construct the frequency distribution table for the following
data:
13, 6, 12, 9, 11, 14, 2, 8, 18, 16, 9, 13, 17, 11, 19, 6, 7, 12, 22, 21, 18, 1, 8, 12, 18.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 12

Question 7.
Given below are the marks secured by 35 students in a surprise test:
41, 32, 35, 21, 11, 47, 42, 00, 05, 18, 25, 24, 29, 38, 30, 04, 14, 24, 34, 44, 48, 33, 36, 38, 41, 48, 08, 34, 39, 11, 13, 27, 26, 43, 03.
Taking class intervals 0-10, 10-20, …….. construct frequency distribution table. Find the number
of students obtaining below 20 marks.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 13

Question 8.
The electricity bills (in ?) of 40 houses in a locality are given below:
78, 87,81,52, 59, 65, 101, 108, 115, 95, 98, 65,62, 121, 128, 63,76, 84, 89,91,65, 101,95,81, 87, 105, 129, 92, 75, 105, 78, 72, 107, 116, 127, 100, 80, 82, 61, 118 Construct a grouped frequency distribution table of class size 10.
Class intervals (Electricity bill in ?) Tally marks Frequency (Number of houses)
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 14

Question 9.
Draw a histogram for the frequency table made for data in Question 8, and answer the following questions:
(i) Which group has the maximum number of houses?
(ii) How many houses pay less than ₹ 100?
(iii) How many houses pay ₹ 100 or more?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 15

Question 10.
The weights of 29 patients in a hospital were recorded as follows:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 16
Draw a histogram to represent this data visually.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 17
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 18

Question 11.
In a study of diabetic patients, the following data was obtained:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 19
Represent the above data by a histogram.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 20
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 21

Question 12.
The histogram showing the weekly wages (in ₹) of workers in a factory is given alongside:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 22
Answer the following:
(i) What is the frequency of class 400-425?
(ii) What is the class having a minimum frequency?
(iii) How many workers get more than ₹425?
(iv) How many workers get less than ₹475?
(v) Number of workers whose weekly wages are more than or equal to ₹400 but less than ₹450.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 23

Question 13.
The number of hours for which students of a particular class watched television during holidays is shown in the histogram below.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 24
Answer the following:
(i) For how many hours did the maximum number of students watch T.V.?
(ii) How many students watched T.V. for less than 4 hours?
(iii) How many students spent more than 5 hours in watching T.V.?
(iv) How many students spent more than 2 hours but less than 4 hours in watching T.V.?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 25

Question 14.
The number of literate females in the age group of 10 to 40 years in a town is shown in the histogram alongside.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 26
Answer the following questions:
(i) Write the classes assuming all the classes are of equal width.
(ii) What is the class size?
(iii) In which age group are the literate females the least?
(iv) In which age group is the number of literate females the highest?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 19 Data Handling Ex 19.1 27

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress

Question 1.
A square field of side 65 m and rectangular field of length 75 m have the same perimeter. Which field has a larger area and by how much?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 1

Question 2.
The shape of a top surface of the table is a trapezium. Find the area if its parallel sides are 1.5 m and 2.5 m and the perpendicular distance between them is 0.8 m.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 2

Question 3.
The length and breadth of a hall of a school are 26 m and 22 m respectively. If one student requires 1.1 sq. m area, then find the maximum number of students to be seated in this hall.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 3

Question 4.
It costs ₹936 to fence a square field at ₹7·80 per metre. Find the cost of levelling the field at ₹2.50 per square metre.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 4

Question 5.
Find the area of the shaded portion in the following figures all measurements are given in cm.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 5
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 6
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 7

Question 6.
Area of a trapezium is 160 sq. cm. Lengths of parallel sides are in the ratio 1:3. If smaller of the parallel sides is 10 cm in length, then find the perpendicular distance between them.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 8

Question 7.
The area of a trapezium is 729 cm2 and the distance between two parallel sides is 18 cm. If one of its parallel sides is 3 cm shorter than the other parallel side, find the lengths of its parallel sides.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 9

Question 8.
Find the area of the polygon given in the figure:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 10
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 11
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 12

Question 9.
The diagonals of a rhombus are 16 m and 12 m, find:
(i) it’s area
(ii) length of a side
(iii) perimeter.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 13

Question 10.
The area of a parallelogram is 98 cm2. If one altitude is half the corresponding base, determine the base and the altitude of the parallelogram.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 14

Question 11.
Preeti is painting the walls and ceiling of a hall whose dimensions are 18 m × 15 m × 5 m. From each can of paint 120 m2 of area is painted. How many cans of paint does she need to paint the hall?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 15

Question 12.
A rectangular paper is size 22 cm × 14 cm is rolled to form a cylinder of height 14 cm, find the volume of the cylinder. (Take π = \(\frac{22}{7}\))
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 16

Question 13.
A closed rectangular wooden box has inner dimensions 90 cm by 80 cm by 70 cm. Compute its capacity and the area of the tin foil needed to line its inner surface.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 17

Question 14.
The lateral surface area of a cuboid is 224 cm2. Its height is 7 cm and the base is a square. Find
(i) side of the square base
(ii) the volume of the cuboid.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 18

Question 15.
The inner dimensions of a closed wooden box are 2 m by 1.2 m by 0.75 m. The thickness of the wood is 2.5 cm. Find the cost of wood required to make the box if 1 m3 of wood costs ₹5400.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 19

Question 16.
A car has a petrol tank 40 cm long, 28 cm wide and 25 cm deep. If the ful consumption of the car averages 13.5 km per litre, how far can the car travel with a full tank of petrol?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 20

Question 17.
The diameter of a garden roller is 1.4 m and it is 2 m long. How much area it will cover in 5 revolutions?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 21

Question 18.
The capacity of an open cylindrical tank is 2079 m3 and the diameter of its base is 21m. Find the cost of plastering its inner surface at ₹40 per square metre.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 22

Question 19.
A solid right circular cylinder of height 1.21 m and diameter 28 cm is melted and recast into 7 equal solid cubes. Find the edge of each cube.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 23

Question 20.
(i) How many cubic metres of soil must be dug out to make a well 20 m deep and 2 m in diameter?
(ii) If the inner curved surface of the well in part (i) above is to be plastered at the rate of ₹50 per m2, find the cost of plastering.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Check Your Progress 24

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions

Mental Maths
Question 1.
Fill in the blanks:
(i) Area of a parallelogram = base × …….
(ii) Area of a trapezium = \(\frac{1}{2}\) × ……….. × distance between parallel sides.
(iii) Area of a rhombus = \(\frac{1}{2}\) × product of ……..
(iv) Area is measured in ……….. units.
(v) Volume of a solid is the measurement of ………… occupied by it.
(vi) Volume is measured in ………… units.
(vii) The volume of a unit cube is ……….
(viii) 1 litre = …………… cm3
(ix) 1 m3 = ………… litres
(x) Volume of a cuboid = ……….. × height.
(xi) Cylinders in which line segment joining the centres of the circular faces is perpendicular to the base are called ……….
(xii) Volume of a cylinder = area of base × ………..
(xiii) Area of four walls = perimeter of floor × …….
(xiv) Lateral surface area of a cube = 4 × (…………)2
(xv) Total surface area of a cylinder of radius r and height h is ………..
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 1

Question 2.
State which of the following statements are true (T) or false (F):
(i) Perimeter of a rectangle is the sum of lengths of its four sides.
(ii) Area of a quadrilateral can be found by splitting it into two triangles.
(iiii) Perimeter of a circle of radius r = πr2.
(iv) Volume of a cube = 6 × (side)2
(v) 1 m3 = 100000 cm3
(vi) Total surface area of a cuboid
= 2 (lb + bh + hl)
(vii) There is no difference between volume and capacity.
(viii)Total surface area of a cylinder = lateral surface area + area of two circular ends.
(ix) Surface area of a cube = 4 × (side)2
(x) Lateral surface area of a cuboid = perimeter of base × height.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 2

Multiple Choice Questions
Choose the correct answer from the given four options (3 to 17):
Question 3.
Area of a triangle is 30 cm2. If its base is 10 cm, then its height is
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 3

Question 4.
If the perimeter of a square is 80 cm, then its area is
(a) 800 cm2
(b) 600 cm2
(c) 400 cm2
(d) 200 cm2
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 4

Question 5.
Area of a parallelogram is 48 cm2. If its height is 6 cm then its base is
(a) 8 cm
(b) 4 cm
(c) 16 cm
(d) none of these
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 5

Question 6.
If d is the diameter of a circle, then its area is
(a) πd2
(b) \(\frac{\pi d^{2}}{2}\)
(c) \(\frac{\pi d^{2}}{4}\)
(d) 2πd2
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 6

Question 7.
If the area of a trapezium is 64 cm2 and the distance between parallel sides is 8 cm, then sum of its parallel sides is
(a) 8 cm
(b) 4 cm
(c) 32 cm
(d) 16 cm
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 7

Question 8.
Area of a rhombus whose diagonals are 8 cm and 6 cm is
(a) 48 cm2
(b) 24 cm2
(c) 12 cm2
(d) 96 cm2
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 8

Question 9.
If the lengths of diagonals of a rhombus is doubled, then area of rhombus will be
(a) doubled
(b) tripled
(c) four times
(d) remains same
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 9

Question 10.
If the length of a diagonal of a quadrilateral is 10 cm and lengths of the perpendiculars on it from opposite vertices are 4 cm and 6 cm, then area of quadrilateral is
(a) 100 cm2
(b) 200 cm2
(c) 50 cm2
(d) none of these
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 10

Question 11.
Area of a rhombus is 90 cm2. If the length of one diagonal is 10 cm then the length of other diagonal is
(a) 18 cm
(b) 9 cm
(c) 36 cm
(d) 4.5 cm
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 11

Question 12.
If the volume of a cube is 729 cm3, then its surface area is
(a) 486 cm2
(b) 324 cm2
(c) 162 cm2
(d) none of these
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 12

Question 13.
If the lateral surface area of a cube is 100 cm2, then its volume is
(a) 25 cm3
(b) 125 cm3
(c) 625 cm3
(d) none of these
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 13

Question 14.
If the length of side of a cube is doubled, then the ratio of volumes of new cube and original cube is
(a) 1 : 2
(b) 2 : 1
(c) 4 : 1
(d) 8 : 1
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 14

Question 15.
If the dimensions of a rectangular room are 10m × 12m × 9m, then the cost of painting its four walls at the rate of ₹8 per m2 is
(a) ₹3186
(b) ₹3618
(c) ₹3168
(d) none of these
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 15

Question 16.
Volume of a cylinder is 1848 cm2. If the diameter of its base is 14 cm, then the height of the cylinder is
(a) 12 cm
(b) 6 cm
(c) 3 cm
(d) none of these
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 16

Question 17.
If the radius of a cylinder is doubled and height is halved, then new volume is
(a) same
(b) 2 times
(c) 4 times
(d) 8 times
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 17

Value Based Questions
Question 1.
Pulkit painted four walls and roof of a rectangular room of size 10m × 12m × 12m. He got ₹10 per m2 for his work. How much money did he earn? He always gives one-fourth of his income to an orphanage. Find how much money he gave to the orphanage? What values are being promoted?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 18

Question 2.
In a slogan writing competition in a school, Rama wrote the slogan ‘Truth pays, never betrays’ on a trapezium shaped cardboard. If the lengths of parallel sides of trapezium are 60 cm and 80 cm and the distance between them is 50 cm, find the area of trapezium. What are the advantages of speaking truth?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 19

Higher Order Thinking Skills (Hots)
Question 1.
The length of a room is 50% more than its breadth. The cost of carpeting the room at the rate of ₹38.50 m2 is ₹924 and the cost of papering the walls at ₹3.30 m2 is ₹214.50. If the room has one door of dimensions 1 m × 2 m and two windows each of dimensions 1 m × 1.5 m, find the dimensions of the room.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 20
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 21

Question 2.
The barrel of a fountain pen, cylindrical in shape, is 7 cm long and 5 mm in diameter. A full barrel of ink in the pen will be used up when writing 310 words on an average. How many words would use up a bottle of ink containing one-fifth of a litre? Answer correct to the nearest 100 words.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 22
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 23

Question 3.
A cylindrical jar is 20 cm high with an internal diameter 7 cm. An iron cube of edge 5 cm is immersed in the jar completely in the water which was originally 12 cm high. Find the rise in the level of water.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 24

Question 4.
Squares each of side 6 cm are cut off from the four comers of a sheet of tin measuring 42 cm by 30 cm. The remaining portion of the tin sheet is made into an open box by folding up the flaps. Find the capacity of the box.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Objective Type Questions 25

ML Aggarwal Class 8 Solutions for ICSE Maths

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4

Question 1.
The surface area of a cube is 384 cm2. Find
(i) the length of an edge
(ii) volume of the cube.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 1

Question 2.
Find the total surface area of a solid cylinder of radius 5 cm and height 10 cm. Leave your answer in terms of n.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 2

Question 3.
An aquarium is in the form of a cuboid whose external measures are 70 cm × 28 cm × 35 cm. The base, side faces and back face are to be covered with coloured paper. Find the area of the paper needed.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 3

Question 4.
The internal dimensions of the rectangular hall are 15 m × 12 m × 4 m. There are 4 windows each of dimension 2 m × 1.5 m and 2 doors each of dimension 1.5 m × 2.5 m. Find the cost of whitewashing all four walls of the hall, if the cost of whitewashing is ₹5 per m2. What will be the cost of whitewashing if the ceiling of the hall is also whitewashed?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 4

Question 5.
A swimming pool is 50 m in length, 30 m in breadth and 2·5 m in depth. Find the cost of cementing its floor and walls at the rate of ₹27 per square metre.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 5

Question 6.
The floor of a rectangular hall has a perimeter 236 m. Its height is 4·5 m. Find the cost of painting its four walls (doors and windows be ignored) at the rate of Rs. 8.40 per square metre.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 6

Question 7.
A cuboidal fish tank has a length of 30 cm, a breadth of 20 cm and a height of 20 cm. The tank is placed on a horizontal table and it is three-quarters full of water. Find the area of the tank which is in contact with water.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 7

Question 8.
The volume of a cuboid is 448 cm3. Its height is 7 cm and the base is a square. Find
(i) a side of the square base
(ii) surface area of the cuboid.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 8

Question 9.
The length, breadth and height of a rectangular solid are in the ratio 5 : 4 : 2. If its total surface area is 1216 cm2, find the volume of the solid.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 9

Question 10.
A rectangular room is 6 m long, 5 m wide and 3·5 m high. It has 2 doors of size 1·1 m by 2 m and 3 windows of size 1·5 m by 1·4 m. Find the cost of whitewashing the walls and the ceiling of the room at the rate of ₹5·30 per square metre.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 10

Question 11.
A cuboidal block of metal has dimensions 36 cm by 32 cm by 0·25 m. It is melted and recast into cubes with an edge of 4 cm.
(i) How many such cubes can be made?
(ii) What is the cost of silver coating the surfaces of the cubes at the rate of ₹0·75 per square centimetre?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 11

Question 12.
Three cubes of silver with edges 3 cm, 4 cm and 5 cm are melted and recast into a single cube, find the cost of coating the surface of the new cube with gold at the rate of ₹3·50 per square centimetre?
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 12

Question 13.
The curved surface area of a hollow cylinder is 4375 cm2, it is cut along its height and formed a rectangular sheet of width 35 cm. Find the perimeter of the rectangular sheet.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 13

Question 14.
A road roller has a diameter of 0.7 m and its width is 1.2 m. Find the least number of revolutions that the roller must take in order to level a playground of size 120 m × 44 m.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 14

Question 15.
A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label?
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 15
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 16

Question 16.
The sum of the radius and height of a cylinder is 37 cm and the total surface area of the cylinder is 1628 cm2. Find the height and the volume of the cylinder.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 17

Question 17.
The ratio between the curved surface and total surface of a cylinder is 1 : 2. Find the volume of the cylinder, given that its total surface area is 616 cm3.
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 18
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 19

Question 18.
The given figure showed a metal pipe 77 cm long. The inner diameter of the cross-section is 4 cm and the outer one is 4.4 cm.
Find its
(i) inner curved surface area
(ii) outer curved surface area
(iii) total surface area.
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 20
Solution:
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 21
ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 18 Mensuration Ex 18.4 22

ML Aggarwal Class 8 Solutions for ICSE Maths