# 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 cm

^{3}

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 cm

^{3}

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 cm

^{3}

ii)The details given about cube are:Side of cube = 8 cm

Volume of cube = (side)

^{3}= (8)

^{3}= 512 cm

^{3}

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 cm

^{3}

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 cm

^{3}

**Question 3: Find the height of a cuboid of volume 100 cm**^{3}, whose length and breadth are 5cm and 4cm respectively.

^{3}, whose length and breadth are 5cm and 4cm respectively.

**Solution: **

The details given about cuboid are –

Volume of cuboid = 100cm

^{3}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 cm**^{3} of a liquid?

^{3}of a liquid?

**Solution: **

The details given about cuboid vessel are –

Volume of cuboid vessel = 300cm

^{3}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 cm

^{3}(1 l = 1000cm^{3})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 cm**^{3 }wood. If it be 4 cm long and 3 cm wide. Find its height.

^{3 }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 cm

^{3}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 = xVolume of cube = (side)

^{3}

^{ }= x^{3}When edge is halved,

Volume of cube = (x / 2)

^{3}

^{ }= x^{3 }/ 8Hence, it means that when edge is halved then volume becomes 1 / 8 times of initial volume.

ii)Let the side of the cube = xVolume of cube = (side)

^{3}= x

^{3}When edge is trebled,

Volume of cube = (3x)

^{3}= 27x

^{3}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 = lLet 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 = lLet 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 cm

^{3}Volume of second cuboid = 4 * 7 * 8 = 224 cm

^{3}Volume of third cuboid = 2 * 3 * 13 = 78 cm

^{3}Volume of cube = Volume of first cuboid + Volume of second cuboid + Volume of third cuboid

= 210 + 224 + 78

= 512 cm

^{3}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 cm**^{3 }of iron weighs 8 gm.

^{3 }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 cm

^{3}Weight of 1 cm

^{3}of iron = 8 gmWeight of 20000 cm

^{3}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 cm

^{3}Volume of cubical block = (side)

^{3}= (25)

^{3}= 15625 cm

^{3}Number of cubical blocks = Volume of log of wood / Volume of cubical block

= 1125000 / 15625

= 72 blocks

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