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 cm³

2000 cm³ = 2000/1000000 m³ = 0.002 m³

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 m³

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 m³ Or 1800000 litres

Amount 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 m³

The length of rectangular field = 70 m

The width of rectangular field = 60 m

Let level of earth rise up by h m in the rectangular field

So, 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 m³

Let level of water rise up by h m

So, 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 = 0.6m³

Let the thickness of beam is h m

So, 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 m²

So, area of field = 30000 m²

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 = 1800m³

Or 1800000 litres

Hence, 18 × 10⁵ 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 cm³

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 m³ = 911250 cm³

The side of cube = 45 cm 

So, the volume of cube = (side)³

= 91125 cm³

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 cm³ 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 cm³

Since weight of 1 cm³ = 8 gm

So, weight of 7200 cm³ = 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 m³ = ……… cm³
(ii) 1 litre = ……. cubic decimetre
(iii) 1 kl = …… m³
(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

Solution:

i) 1 m³ = 1000000 cm³

ii) 1 litre = 1 cubic decimetre

iii) 1 kl = 1 m³

iv) The volume of a cube of side 8 cm is 8 × 8 × 8 = 512 cm³

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

Volume/ length × breadth = 4000/ 10 × 8 = 50 cm

vi) 1 cu.dm = 1000000 cu.mm

vii) 1 cu.km = 1000000000 cu.m

viii) 1 litre = 1000 cu.cm

ix) 1 ml = 1 cu.cm

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