## RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQS

These Solutions are part of RD Sharma Class 9 Solutions. Here we have given RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQS

Other Exercises

- RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.1
- RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2
- RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder VSAQS
- RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQS

Mark correct alternative in each of the following:

Question 1.

In a cylinder, if radius is doubled and height is halved, curved surface area will be

(a) halved

(b) doubled

(c) same

(d) four times

Solution:

Let radius of the first cylinder (r_{1}) = r

and height (h_{1}) = h

Surface area = 2πrh

If radius is doubled and height is halved

∴ Their surface area remain same (c)

Question 2.

Two cylindrical jars have their diameters in the ratio 3:1, but height 1:3. Then the ratio of their volumes is

(a) 1 : 4

(b) 1 : 3

(c) 3 : 1

(d) 2 : 5

Solution:

Sol. Ratio in the diameters of two cylinder = 3:1

and ratio in their heights = 1:3

Let radius of the first cylinder (r_{1}) = 3x

and radius of second (r_{2}) = x

and height of the first (h_{1}) = y

and height of the second (h_{2}) = 3y

Now volume of the first cylinder = πr^{2}h

= π(3x)^{2} x y = 9πx^{2}y

and of second cylinder = π(x^{2}) (3y)

∴ Ratio between then = 9πx^{2}y : 3πx^{2}y

= 3 : 1 (c)

Question 3.

The number of surfaces in right cylinder is

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

The number of surfaces of a right cylinder is three. (c)

Question 4.

Vertical cross-section of a right circular cylinder is always a

(a) square

(b) rectangle

(c) rhombus

(d) trapezium

Solution:

The vertical cross-section of a right circular cylinder is always a rectangle. (b)

Question 5.

If r is the radius and h is height of the cylinder the volume will be

Solution:

Volume of a cylinder = πr^{2}h (b)

Question 6.

The number of surfaces of a hollow cylindrical object is

(a) 1

(b) 2

(c) 3

(d) 4

Solution:

The number of surfaces of a hollow cylindrical object is 4. (d)

Question 7.

If the radius of a cylinder is doubled and the height remains same, the volume will be

(a) doubled

(b) halved

(c) same

(d) four times

Solution:

If r be the radius and h be the height, then volume = πr2h

If radius is doubled and height remain same,

the volume will be

= π(2r)^{2}h = π x 4r^{2}h

= 4πr^{2}h = 4 x Volume

The volume is four times (d)

Question 8.

If the height of a cylinder is doubled and radius remains the same, then volume will be

(a) doubled

(b) halved

(c) same

(d) four times

Solution:

If r be the radius and h be the height, then volume of a cylinder = πr^{2}h

If height is doubled and radius remain same, then volume = πr^{2}(2h) = 2πr^{2}h

∴ Its doubled (a)

Question 9.

In a cylinder, if radius is halved and height is doubled, the volume will be

(a) same

(b) doubled

(c) halved

(d) four times

Solution:

Let r be radius and h be height, then Volume = πr^{2}h

If radius is halved and height is doubled

Question 10.

If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is

Solution:

Let diameter of the base of a cylinder (r) = h

Then its height (h) = h

Question 11.

A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m^{2}, is

(a) 40π

(b) 80π

(c) 160π

(d) 200π

Solution:

Diameter of a cylindrical tunnel = 2 m

∴ Radius (r) = \(\frac { 2 }{ 2 }\) = 1m

and length (h) = 40 m

Curved surfae area = 2πrh = 2 x π x 1 x 40 = 80π (b)

Question 12.

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. Ratio of their radii is

Solution:

Let r_{1} and h_{1} be the radius and height of the

first cylinder, then

Volume = πr_{1}^{2}h_{1}

Similarly r_{1} and h_{2} are the radius and height of the second cylinder

∴ Volume = πr^{2}h_{2}

But their volumes are equal,

Question 13.

The radius of a wire is decreased to one- third. If volume remains the same, the length will become

(a) 3 times

(b) 6 times

(c) 9 times

(d) 27 times

Solution:

In the first case, r and h1, be the radius and height of the cylindrical wire

∴ Volume = πr^{2}h_{1} …(i)

In second case, radius is decreased to one third

∴ In second case height is 9 times (c)

Question 14.

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?

Solution:

Let r be the radius and h be the height then volume = πr^{2}h

If height is doubled and volume is same and let x be radius then πr^{2}h = π(x)^{2} x 2h

Question 15.

The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?

Solution:

Let r be the radius and h be the height, then volume = πr^{2}h

This volume is \(\frac { 1 }{ 4 }\) of the volume of a rectangular box

∴ Volume of box = 4πr^{2}h

Let side of base of box = x and height h,

then volume = x^{2}h

∴ 4πr^{2}h = x^{2}h

Question 16.

The height ft of a cylinder equals the circumference of the cylinder. In terms of ft, what is the volume of the cylinder?

Solution:

In a cylinder,

h = circumference of the cylinder

Question 17.

A cylinder with radius r and height ft is closed on the top and bottom. Which of the following expressions represents the total surface area of this cylinder?

(a) 2πr(r + h)

(b) πr(r + 2h)

(c) πr(2r + h)

(d) 2πr^{2} + h

Solution:

r is the radius of the base and ft is the height of a closed cylinder

Then total surface area = 2πr(r + h ) (a)

Question 18.

The height of sand in a cylindrical-shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?

Solution:

Let h be the height and d be the diameter of a cylinder, then

Question 19.

Two steel sheets each of length a_{1} and breadth a_{2} are used to prepare the surfaces of two right circular cylinders – one having volume v_{1 }and height a_{2} and other having volume v_{2} and height a_{1}. Then,

Solution:

Length of each sheet = a_{1}

and breadth = a_{2}

Volume of cylinder = πr^{2}h

In first case,

v_{1} is volume and a_{2} is the height

Question 20.

The altitude of a circualr cylinder is increased six times and the base area is decreased to one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is

Solution:

In first case,

Let r be the radius and h be the height of the cylinder. Then,

∴ Lateral surface area = 2πrh

In second case,

Hope given RD Sharma Class 9 Solutions Chapter 19 Surface Areas and Volume of a Circular Cylinder MCQS are helpful to complete your math homework.

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