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# Class 8 RD Sharma Solutions – Chapter 21 Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube) – Exercise 21.1 | Set 1

### 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

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

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

### Chapter 21 Mensuration II (Volume and Surface Areas of a Cuboid and a Cube) – Exercise 21.1 | Set 2

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