# Class 8 RD Sharma Solutions – Chapter 21 Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube) – Exercise- 21.2 | Set 2

**Question 11. How many bricks each of size 25 cm x 10 cm x 8 cm will be required to build a wall 5 m long, 3 m high**,** and 16 cm thick assuming that the volume of sand and cement used in the construction is negligible?**

**Solution:**

Given, length of brick = 25 cm

The breadth of brick = 10 cm

The height of brick = 8 cm

So, the volume of 1 brick = l × b × h

= 25 × 10 × 8 = 2000 cm

^{3}2000 cm

^{3}= 2000/1000000 m^{3}= 0.002 m^{3}Given, length of the wall = 5 m

The breadth of the wall = 16 cm = 0.16 m

The height of the wall = 3 m

So, the volume of wall = l × b × h= 5 × 0.16 × 3 = 2.4 m

^{3}Number of bricks required = Volume of wall/ Volume of 1 brick

= 2.4/0.002 = 1200

Hence, 1200 bricks are required to build up the wall.

**Question 12. A village, having a population of 4000 requires 150 litres water per head per day. It has a tank which is 20 m long, 15 m broad and 6 m high. For how many days the water of this tank will last?**

**Solution:**

Given, length of tank = 20 m

The width of tank = 15 m

The height of tank = 6 m

So, the volume of water tank = l × b × h = 20 × 15 × 6

= 1800 m

^{3}Or 1800000 litresAmount of water consumed by 1 villager = 150 litres

So, amount of water consumed by 4000 villagers = 150 × 4000 = 600000 litres

Number of days the water will end = Volume of water tank/ Amount of water consumed by villagers

= 1800000/ 600000 = 3 days

Hence, the water in tank will last till 3 days

**Question 13. ****A rectangular field is 70 m long and 60 m broad. A well of dimensions 14 m × 8 m × 6 m is dug outside the field and the earth dugout from this well is spread evenly on the field. How much will the earth level rise?**

**Solution:**

Given, length of well= 14 m

The width of well = 8 m

The height of well = 6 m

Volume of well = Volume of Earth dugout = l × b × h

= 14 × 8 × 6 = 672 m

^{3}The length of rectangular field = 70 m

The width of rectangular field = 60 m

Let level of earth rise up by

hm in the rectangular fieldSo, 70 × 60 × h = 672

= 0.16 m or 16 cm

Hence, the level of Earth rise up by 16 cm

**Question 14. A swimming pool is 250 m long and 130 m wide. 3250 cubic meters of water is pumped into it. Find the rise in the level of water.**

**Solution:**

Given, length of pool = 250 m

The width of pool = 130 m

Volume of water in pool = 3250 m

^{3}Let level of water rise up by

hmSo, 250 × 130 × h = 3250

h = 0.1 m or 10 cm

Hence, the water level in pool rise up by 10 cm

**Question 15. A beam 5 m long and 40 cm wide contains 0.6 cubic meters of wood. How thick is the beam?**

**Solution:**

Given, length of beam = 5 m

The breadth of beam = 40 cm = 0.4m

Volume of wood in beam = 0.6m

^{3}Let the thickness of beam is

hmSo, 5 × 0.4 × h = 0.6

h = 0.3 m or 30 cm

Hence, the thickness of beam is 30 cm

**Question 16. The rainfall on a certain day was 6 cm. How many litres of water fell on 3 hectares of field on that day?**

**Solution:**

Given, the area of field = 3 hectares

As 1 hectare = 10000 m

^{2}So, area of field = 30000 m

^{2}And the height of rain fall = 6 cm = 0.06 m

Amount of rain water fell on that day = Volume of rain water

= Area of field X height of rainfall = 30000 × 0.06 = 1800m

^{3}Or 1800000 litres

Hence, 18 × 10^{5}litres of rain water fell on the field

**Question 17. An 8 m long cuboidal beam of wood when sliced produces four thousand 1 cm cubes and there is no wastage of wood in this process. If one edge of the beam is 0.5 m, find the third edge.**

**Solution: **

Given, length of cuboidal beam = 8 m = 800 cm

The second edge of beam = 0.5 m = 50 cm

Number of small cubes so formed = 4000

Side of 1 cube = 1 cm

So, Volume of beam = Volume of small cubes = 4000 × Volume of 1 cube

= 4000 × (1 × 1 × 1) = 4000 cm

^{3}So, we can state

Third edge of beam = Volume of beam/ (length of beam × second edge of beam)

= 4000/ 800 × 50 = 0.1 cm

Hence, the third edge of beam is 0.1 cm long

**Question 18. The dimensions of a metal block are 2.25 m by 1.5 m by 27 cm. It is melted and recast into cubes, each of the side 45 cm. How many cubes are formed?**

**Solution:**

Given, length of block = 2.25 m

The width of block = 1.5 m

The height of block = 27 cm = 0.27 m

So, Volume of metal block = l × b × h = 2.25 × 1.5 × 0.27

= 0.91125 m

^{3}= 911250 cm^{3}The side of cube = 45 cm

So, the volume of cube = (side)

^{3}= 91125 cm

^{3}Number of cubes that can be formed = Volume of metal block/ Volume of 1 cube

= 911250/91125 = 10

Hence, 10 cubes are formed from the metal block

**Question 19. A solid rectangular piece of iron measures 6 m by 6 cm by 2 cm. Find the weight of this piece if 1 cm**^{3} of iron weighs 8 gm.

^{3}of iron weighs 8 gm.

**Solution:**

Given, length of rectangular piece = 6 m = 600 cm

The breadth of rectangular piece = 6 cm

The height of rectangular piece = 2 cm

So, Volume of rectangular piece = 600 × 6 × 2 = 7200 cm

^{3}Since weight of 1 cm

^{3}= 8 gmSo, weight of 7200 cm

^{3}= 8 × 7200 = 57600 gm or 57.6 kg

Hence, the weight of iron piece is 57.6 kg

**Question 20. Fill in the blanks in each of the following to make the statement true :**

**(i) 1 m**^{3} = ……… cm^{3}

**(ii) 1 litre = ……. cubic decimetre**

**(iii) 1 kl = …… m**^{3}

**(iv) The volume of a cube of side 8 cm is ……. .**

**(v) The volume of wooden cuboid of length 10 cm and breadth 8 cm is 4000 cm3. The height of the cuboid is ……. cm**

**(vi) 1 cu.dm = ……. cu.mm**

**(vii) 1 cu.km = ……cu.m**

**(viii) 1 litre =……. cu.cm**

**(ix) 1 ml = ……… cu.cm**

**(x) 1 kl = ……… cu.dm = ……. cu.cm**

^{3}= ……… cm

^{3}

^{3}

**Solution:**

i)1 m^{3}=1000000cm^{3}

ii)1 litre =1cubic decimetre

iii)1 kl =1m^{3}

iv)The volume of a cube of side 8 cm is 8 × 8 × 8 =512 cm^{3}

v)The volume of wooden cuboid of length 10 cm and breadth 8 cm is 4000 cm^{3}. The height of the cuboid isVolume/ length × breadth = 4000/ 10 × 8 =

50cm

vi)1 cu.dm =1000000cu.mm

vii)1 cu.km =1000000000cu.m

viii)1 litre =1000cu.cm

ix)1 ml =1cu.cm

x)1 kl =1000cu.dm =1000000cu.cm

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