## RD Sharma Class 8 Solutions Chapter 21 Mensuration II (Volumes and Surface Areas of a Cubiod and a Cube) Ex 21.1

These Solutions are part of RD Sharma Class 8 Solutions. Here we have given RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.1

Other Exercises

Question 1.
Find the volume of a cuboid whose
(i) length = 12 cm, breadth = 8 cm, height = 6 cm
(ii) length = 1.2 m, breadth = 30 cm, height = 15 cm
(iii) length = 15 cm, breadth = 2.5 dm, height = 8 cm

Solution:
In a cuboid,
(i) Length (l) = 12 cm
Height (h) = 6 cm
∴ Volume = Ibh = 12 x 8 x 6 cm3 = 576 cm3
(ii) Length (l) = 1.2 m = 120 cm
Height (h) = 15 cm
∴ Volume = Ibh = 120 x 30 x 15 cm3 = 54000 cm3
(iii) Length (l) = 15 cm
Breadth (b) = 2.5 dm = 25 cm
Height (h) = 8 cm
∴ Volume = Ibh
= 15 x 25 x 8 cm3 = 3000 cm2

Question 2.
Find the volume of the cube whose side is
(i) 4 cm
(ii) 8 cm
(iii) 1.5 dm
(iv) 1.2 m
(v) 25 mm.
Solution:
(i) Side of a cube (a) = 4 cm
∴ Volume = a3 = (4)3 cm3 = 4 x 4 x 4 = 64 cm3

(ii) Side of cube (a) = 8 cm
∴ Volume = a3 = (8)3 4 cm
= 8 x 8 x 8 cm3 = 512 cm3
(iii) Side of cube (a) = 1.5 dm = 15 cm
∴ Volume = a3 = (1.5)3 dm2 = (15)3 cm3
= 15 x 15 x 15 = 3375 cm3
(iv) Side of cube (a) = 1.2 m = 120 cm
∴ Volume = a3 = (120)3 cm3
= 120 x 120 x 120 = 1728000 cm3
(v) Side of cube (a) = 25 mm = 2.5 cm.
∴ Volume = a3 = (2.5)3 cm3
= 2.5 x 2.5 x 2.5 cm3 = 15.625 cm3

Question 3.
Find the height of a cuboid of volume 100 cm3 whose length and breadth are 5 cm and 4 cm respectively.
Solution:
Volume of a cuboid =100 cm3
Length (1) = 5 cm
and breadth (b) = 4 cm

Question 4.
A cuboidal vessel is 10 cm long and 5 cm wide, how high it must be made to hold 300 cm3 of a liquid ?
Solution:
Volume of the liquid in the vessel = 300 cm3
Length (l)= 10 cm

Question 5.
A milk container is 8 cm long and 50 cm wide. What should be its height so that it can hold 4 litres of milk ?
Solution:
Capacity of milk = 4 litres
∴ Volume of the container = 4 x 1000 cm3 = 4000 cm3
Length (l) = 8 cm
Width (b) = 50 cm

Question 6.
A cuboidal wooden block contains 36 cm3 wood. If it be 4 cm long and 3 cm wide, find its height.
Solution:
Volume of wooden cuboid block = 36 cm3
Length (l) = 4 cm

Question 7.
What will happen to the volume of a cube, if its edge is (i) halved (ii) trebled ?
Solution:
Let side of original cube = a cm
∴ Volume = a3 cm3
(i) In first case,

(ii) In second case, when side (edge) is trebled, then side = 3a
∴ Volume = (3a)3 = 27a3
∴ It will be 27 times

Question 8.
What will happen to the volume of a cuboid if its (i) Length is doubled, height is same and breadth is halved ? (ii) Length is doubled, height is doubled and breadth is same ?
Solution:
Let l, b and h be the length, breadth and height of the given cuboid respectively.
∴ Volume = lbh.
(i) Length is doubled = 21

∴ The volume will be the same.
(ii) Length is doubled = 21
breadth is same = b height is doubled = 2h
∴ Volume = 2l x b x 2h = 4 lbh
∴ Volume will be 4 times

Question 9.
Three cuboids of dimensions 5 cm x 6 cm x 7 cm, 4 cm x 7 cm * 8 cm and 2 cm x 3 cm x 13 cm are melted and a cube is made. Find the side of cube.
Solution:
Dimensions of first cuboid = 5 cm x 6 cm x 7 cm
∴ Volume = 5 x 6 x 7 = 210 cm3
Dimensions of second cuboid = 4 cm x 7 cm x 8 cm
∴ Volume = 4x 7 x 8 = 224 cm3
Dimensions of third cuboid = 2 cm x 3 cm x 13 cm
∴ Volume = 2 x 3 x 13 = 78 cm3
Total volume of three cubes = 210 + 224 + 78 cm3 = 512 cm3
∴ Volume of cube = 512 cm3

Question 10.
Find the weight of solid rectangular iron piece of size 50 cm x 40 cm x 10 cm, if 1 cm3 of iron weighs 8 gm.
Solution:
Dimension of cuboidal iron piece = 50 cm x 40 cm x 10 cm
∴ Volume = 50 x 40 x 10 = 20000 cm3
Weight of 1 cm3 = 8 gm
∴ Total weight of piece = 20000 x 8 gm

Question 11.
How many wooden cubical blocks of side 25 cm can be cut from a log of wood of size 3 m by 75 cm by 50 cm, assuming that there is no wastage ?
Solution:
Length of log (l) = 3 m = 300 cm.
and height (h) = 50 cm
∴ Volume of log = lbh = 300 x 75 x 50 cm3 = 1125000 cm3
Side of cubical block = 25 cm
∴ Volume of one block = a2 = 25 x 25 x 25 cm3 = 15625 cm3
∴ Number of blocks to be cut out

Question 12.
A cuboidal block of silver is 9 cm long, 4 cm broad and 3.5 cm in height. From it, beads of volume 1.5 cm2 each are to be made. Find the number of beads that can be made from the block ?
Solution:
Length of block (l) = 9 cm
and height (h) = 3.5 cm
∴ Volume = l x b x h = 9 x 4 x 3.5 cm3 = 126 cm3
Volume of one bead = 1.5 cm3
∴ Number of beads = $$\frac { 126 }{ 105 }$$ = 84

Question 13.
Find the number of cuboidal boxes measuring 2 cm by 3 cm by 10 cm which can be stored in a carton whose dimensions are 40 cm, 36 cm and 24 cm.
Solution:
Length of cuboidal box (l) = 2 cm
and height (h) = 10 cm
∴ Volume = lx b x h = 2 x 3 x 10 = 60 cm3
Volume of carton = 40 x 36 x 24 cm3
= 34560 cm3
∴ Number of boxes to be height in the carton

Question 14.
A cuboidal block of solid iron has dimensions 50 cm, 45 cm and 34 cm. How many cuboids of size 5 cm by 3 cm by 2 cm can be obtained from the block ? Assume cutting causes no wastage.
Solution:
Dimensions of block = 50 cm, 45 cm, 34 cm
∴ Volume = 50 x 45 x 34 = 76500 cm3
Size of cuboid = 5 cm x 3 cm x 2 cm
∴ Volume of cuboid =  5 x 3 x 2 = 30 cm3

Question 15.
A cube A has side thrice as long as that of cube B ? What is the ratio of the volume of cube A to that of cube B ?
Solution:
Let side of cube B = a
Then Volume = a3
and side of cube A = 3a
Volume = (3a)3 = 3a x 3a x 2a = 27a3
∴ Ratio of volume’s A and B = 27a3 : a3
= 27 : 1

Question 16.
An ice-cream brick measures 20 cm by 10 cm by 7 cm. How many such bricks can be stored in a deep fridge whose inner dimensions are 100 cm by 50 cm by 42 cm ?
Solution:
Dimensions of ice cream brick = 20 cm x 10 cm x 7 cm
∴ Volume = 20 x 10 x 7 cm3 = 1400 cm3
Dimensions of inner of fridge = 100 cm x 50 cm x 42 cm = 210000 cm3
∴ Number of bricks to be kept in the fridge

Question 17.
Suppose that there are two cubes, having edges 2 cm and 4 cm, respectively. Find the volume V1 and V2 of the cubes and compare them.
Solution:
Side of first cube (a) = 2 cm
∴ Volume (V1) = a3 = (2) = 8 cm3
Similarly side of second cube = 4 cm
and volume (V2) = (4)3 = 64 cm3
Now V2 = 64 cm3 = 8 x 8 cm3
= 8 x V1
⇒ V2 = 8V1

Question 18.
A tea-packet measures 10 cm x 6 cm x 4 cm.How many such tea-packets can be placed in a cardboard box of dimensions 50 cm x 30 cm x 0.2 m ?
Solution:
Dimensions of tea-packet = 10cm x 6cm x 4 cm
∴ Volume =10 x 6 x 4 = 240 cm3
Dimensions of box = 50 cm x 30 cm x 0.2 m
= 50 cm x30 cm x20 cm
∴ Volume = 50 x 30 x 20 = 30000 cm3
∴ Number of tea-packets to be kept = $$\frac { 30000 }{ 240 }$$

Question 19.
The weight of a metal block of size 5 cm by 4 cm by 3 cm is 1 kg. Find the weight of a block of the same metal of size 15 cm by 8 cm by 3 cm.
Solution:
Dimensions of a metal block = 5 cm x 4 cm x 3 cm = 5 x 4 x 3 = 60 cm3
Dimensions of a second block = 15 cm x 8 cm x 3 cm = 15 x 8 x 3 = 360 cm3
But weight of first block = 1 kg
∴ Weight of second block
= $$\frac { 1 }{ 16 }$$ x 360 = 6 kg

Question 20.
How many soap cakes can be placed in a box of size 56 cm x 0.4 m x 0.25 m, it the size of soap cake is 7 cm x 5 cm x 2.5 cm ?
Solution:
Size of box = 56 cm x 0.4 m x 0.25 m = 56 cm x 40 cm x 25 cm
∴ Volume = 56 x 40 x 25 cm3 = 56000 cm3
Size of a soap cake = 7 cm x 5 cm x 2.5 cm
∴ Volume = 7 x 5 x 2.5 cm3 = 87.5 cm3
∴ Number of cakes to be kept in the box
= $$\frac { 56000 }{ 87.5 }$$ = 640

Question 21.
The volume of a cuboid box is 48 cm3. If its height and length are 3 cm and 4 cm respectively, find its breadth.
Solution:
Volume of cuboid box = 48 cm3
Length (l) = 4 cm
Height = (h) = 3 cm

Hope given RD Sharma Class 8 Solutions Chapter 21 Mensuration II Ex 21.1 are helpful to complete your math homework.

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