Class 8 RD Sharma Solutions Chapter 21 Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube) Exercise 21.1 | Set 1 (original) (raw)
Last Updated : 23 Jul, 2025
Question 1: Find the volume of cuboid whose:
i) length = 12 cm, breadth = 8 cm and height = 6 cm
ii) length = 1.2 m, breadth = 30 cm and height = 15 cm
iii) length = 1.5 dm, breadth = 2.5 dm and height = 8 cm
Solution:
i) The details given about cuboid are -
Length of cuboid = 12 cm
Breadth of cuboid = 8 cm
Height of cuboid = 6 cm
Volume of cuboid = length * breadth * height
= 12 * 8 * 6
= 576 cm3
ii) The details given about cuboid are-
Length of cuboid = 1.2 m = 120 cm (1 m = 100 cm)
Breadth of cuboid = 30 cm
Height of cuboid = 15 cm
Volume of cuboid = length * breadth * height
= 120 * 30 * 15
= 54000 cm3
iii) The details given about cuboid are -
Length of cuboid = 1.5 dm = 15 cm (1 dm = 10 cm)
Breadth of cuboid = 2.5 dm = 25 cm (1dm = 10 cm)
Height of cuboid = 8 cm
Volume of cuboid = length * breadth * height
= 15 * 25 * 8
= 3000 cm3
Question 2: Find the volume of cube whose side is:
i) 4 cm
ii) 8 cm
iii) 1.5 dm
iv) 1.2 m
v) 25 mm
Solution:
i) The details given about cube are:
Side of cube = 4 cm
Volume of cube = (side)3
= (4)3
= 64 cm3
ii) The details given about cube are:
Side of cube = 8 cm
Volume of cube = (side)3
= (8)3
= 512 cm3
iii) The details given about cube are:
Side of cube = 1.5 dm = 15 cm (1 dm = 10 cm)
Volume of cube = (side)3
= (15)3
= 3375 cm3
iv) The details given about cube are -
Side of cube = 1.2 m = 120 cm (1 m = 100 cm)
Volume of cube = (side)3
= (120)3
= 1728000 cm3
v) The details given about cube are -
Side of cube = 25 mm = 25 * 0.1 = 2.5 cm
Volume of cube = (side)3
= (2.5)3
= 15.625 cm3
Question 3: Find the height of a cuboid of volume 100 cm3, whose length and breadth are 5cm and 4cm respectively.
Solution:
The details given about cuboid are -
Volume of cuboid = 100cm3
Length of cuboid = 5 cm
Breadth of cuboid = 4 cm
Let height of cuboid = h
Volume of cuboid = l * b * h
100 = 5 * 4 * h
100 / 20 = h
5cm = h
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:
The details given about cuboid vessel are -
Volume of cuboid vessel = 300cm3
Length of cuboid vessel = 10 cm
Breadth of cuboid vessel = 5 cm
Let height of cuboid vessel = h
Volume of cuboidal vessel = l * b * h
300 = 10 * 5 * h
300 / 50 = h
6 cm = h
Question 5: A milk container is 8 cm long and 50 cm wide. What should be its height so that it can hold 4 liters of milk?
Solution:
The details given about milk container are -
Volume of milk container = 4 l = 4000 cm3 (1 l = 1000cm3)
Length of milk container = 8 cm
Breadth of milk container = 50 cm
Let height of milk container = h
Volume of milk container = l * b * h
4000 = 8 * 50 * h
4000 / 400 = h
10 cm = h
Question 6: A cuboidal wooden block contains 36 cm3 wood. If it be 4 cm long and 3 cm wide. Find its height.
Solution:
The details given about milk container are -
Volume of wooden block = 36 cm3
Length of milk container = 4 cm
Breadth of milk container = 3 cm
Let height of milk container = h
Volume of milk container = l * b * h
36 = 4 * 3 * h
36 / 12 = h
3 cm = h
Question 7: What will happen to the volume of cube, if its edge is:
i) Halved
ii) Trebled
Solution:
i) Let the side of the cube = x
Volume of cube = (side)3
= x3
When edge is halved,
Volume of cube = (x / 2)3
= x3 / 8
Hence, it means that when edge is halved then volume becomes 1 / 8 times of initial volume.
ii) Let the side of the cube = x
Volume of cube = (side)3
= x3
When edge is trebled,
Volume of cube = (3x)3
= 27x3
Hence, it means that when edge is trebled then volume becomes 27 times of initial volume.
Question 8: What will happen to the volume of 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:
i) Let length of cuboid = l
Let breadth of cuboid = b
Let height of cuboid = h
Volume of cuboid = l * b * h
= lbh
When,
length = 2l
height = h
breadth = b / 2
Volume of cuboid = 2 * l * b * h / 2
= lbh
Hence, if length is doubled. Height is same and breadth is halved then it does not affect initial volume.
ii) Let length of cuboid = l
Let breadth of cuboid = b
Let height of cuboid = h
Volume of cuboid = l * b * h
= lbh
When,
Length = 2l
Height = 2h
Breadth = b
Volume of cuboid = 2 * l * 2 * b * h
= 4lbh
Hence, if length is doubled. Height is doubled and breadth then volume becomes 4 times of the initial volume.
Question 9: Three cuboids of the dimension 5 cm * 6 cm * 7 cm , 4 cm * 7 cm * 8 cm and 2 cm * 3 cm * 13 cm are melted and a cube is made. Find the side of the cube.
Solution:
Volume of first cuboid = 5 * 6 * 7 = 210 cm3
Volume of second cuboid = 4 * 7 * 8 = 224 cm3
Volume of third cuboid = 2 * 3 * 13 = 78 cm3
Volume of cube = Volume of first cuboid + Volume of second cuboid + Volume of third cuboid
= 210 + 224 + 78
= 512 cm3
Volume of cube = (side)3
512 = (side)3
8 cm = side
Question 10: Find the weight of a solid rectangular iron piece of size 50 cm * 40 cm * 10 cm, if 1 cm3 of iron weighs 8 gm.
Solution:
The details given about solid rectangular iron piece are -
Length of solid rectangular iron piece = 50 cm
Breadth of solid rectangular iron piece = 40 cm
Height of solid rectangular iron piece = 10 cm
Volume of solid rectangular iron piece = l * b * h
= 50 * 40 * 10
= 20000 cm3
Weight of 1 cm3 of iron = 8 gm
Weight of 20000 cm3 of iron = 20000 * 8
= 160000 gm
= 160 kg (1 kg = 1000 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:
The details given about log of wood are -
Length of log of wood = 3 m = 300 cm (1 m = 100 cm)
Breadth of log of wood = 75 cm
Height of log of wood = 50 cm
Volume of log of wood = l * b * h
= 300 * 75 * 50
= 1125000 cm3
Volume of cubical block = (side)3
= (25)3
= 15625 cm3
Number of cubical blocks = Volume of log of wood / Volume of cubical block
= 1125000 / 15625
= 72 blocks