Class 8 RD Sharma Solutions- Chapter 21 Mensuration II (Volumes and Surface Areas of a Cuboid and a Cube)- Exercise 21.2 | Set 1

Question 1. Find the volume in cubic meters (cu.m) of each of the cuboids whose dimensions are :
(i) length = 12 m, breadth = 10 m, height = 4.5 m
(ii) length = 4 m, breadth = 2.5 m, height = 50 cm
(iii) length = 10 m, breadth = 25 dm, height = 25 cm

Solution:

i) length = 12 m, breadth = 10 m, height = 4.5 m

Since, Length (l) = 12 m

Breadth (b) = 10 m

Height (h) = 4.5 m

As we know, Volume of Cuboid = l × b × h

= 12 × 10 × 4.5 m³ = 540 m³

Hence, Volume of given cuboid is 540 m³

ii) length = 4 m, breadth = 2.5 m, height = 50 cm 

Since, Length (l) = 4 m

Breadth (b) = 2.5 m

Height (h) = 50 cm = 0.5 m

As we know, Volume of Cuboid = l × b × h

= 4 × 2.5 × 0.5 m³ = 5 m³

Hence, Volume of given cuboid is 5 m³

iii) length = 10 m, breadth = 25 dm, height = 25 cm

Since, Length (l) = 10 m

Breadth (b) = 25 dm = 2.5 m

Height (h) = 50 cm = 25 cm = 0.25 m 

As we know, Volume of Cuboid = l × b × h

= 10 × 2.5 × 0.25 m³ = 6.25 m³

Hence, Volume of given cuboid is 6.25 m³

Question 2. Find the volume in cubic decimeter of each of the cubes whose side is
(i) 1.5 m
(it) 75 cm
(iii) 2 dm 5 cm

Solution:

i) 1.5 m

Since the side of cube = 1.5 m

As we know, Volume of Cube = (side)³

= (1.5)³ = 3.375 m³

As 1 m³ = 1000 dm³)

3.375 m³ = 3375dm³

Hence, Volume of the given cube is 3375 dm³

ii) 75 cm

Since the side of cube = 75 cm = 7.5 dm

As we know, Volume of Cube = (side)³

= (7.5)³ = 421.875 dm³

Hence, Volume of the given cube is 421.875 dm³

iii) 2 dm 5 cm

Since the side of cube = 2 dm 5 cm = 2.5 dm

As we know, Volume of Cube = (side)³

= (2.5)³ = 15.625 dm³

Hence, Volume of the given cube is 15.625 dm³

Question 3. How much clay is dug out in digging a well measuring 3 m by 2 m by 5 m?

Solution:

Given, length of well = 3 m

The breadth of well = 2 m

The height of well = 5 m

Amount of clay dig out = Volume of well 

The volume of well = l × b × h = 3 × 2 × 5 m³

= 30 m³

Hence, the amount of clay dug out is 30 m³

Question 4. What will be the height of a cuboid of volume 168 m³, if the area of its base is 28 m²?

Solution:

Volume of cuboid = l × b × h = 168 m³

Area of cuboid = l × b = 28 m²

So, the height of the cuboid can be derived = Volume of cuboid/ Area of cuboid 

h = 168/28 m = 6 m

Hence, the height of the cuboid is 6 m

Question 5. A tank is 8 m long, 6 m broad, and 2 m high. How much water can it contain?

Solution:

Given, length of tank = 8 m

The breadth of tank = 6 m

The height of the tank = 2 m

Amount of water the tank can hold = Volume of tank 

The volume of tank = l × b × h = 8 × 6 × 2 m³

= 96 m³

(As 1 m³ = 1000 liters)

Hence, the amount of water the tank can hold is 96000 liters

Question 6. The capacity of a certain cuboidal tank is 50000 litres of water. Find the breadth of the tank if its height and length are 10 m and 2.5 m respectively.

Solution: 

Given, volume of cuboidal tank = 50000 litres

The height of tank = 10 m

The length of tank = 2.5 m

We need to find breadth of the tank.

As 1 l = 1/1000 m³

So, 50000 l = 50 m³

Volume of cuboidal tank = l × b × h 

50 = 2.5 × b × 10 

b = 2 m 

Hence, the breadth of cuboidal tank is 2 m

Question 7. A rectangular diesel tanker is 2 m long, 2 m wide and 40 cm deep. How many litres of diesel can it hold?

Solution:

Given, length of tanker = 2 m

The breadth of tanker = 2 m

The depth or height of tanker = 40 cm = 0.4 m

Amount of diesel tanker can hold = Volume of cuboidal tanker 

= l × b × h = 2 × 2 × 0.4 = 1.6 m³

And, 1.6 m³ = 1.6 × 1000 = 1600 litres

Hence, the tanker can hold 1600 litres of diesel

Question 8. The length, breadth and height of a room are 5 m, 4.5 m and 3 m, respectively. Find the volume of the air it contains.

Solution:

Given, the length of room = 5 m

The breadth of room = 4.5 m

The height of room = 3 m

Volume of air the room can hold = Volume of Cuboidal room

= l × b × h = 5 × 4.5 × 3 = 67.5 m³

Hence, the volume of air the room can contain is 67.5 m³

Question 9. A water tank is 3 m long, 2 m broad and 1 m deep. How many litres of water can it hold?

Solution:

Given, the length of water tank = 3 m

The breadth of water tank = 2 m

The height of water tank = 1 m

Amount of water the tank can hold = Volume of Cuboidal water tank

= l × b × h = 3 × 2 × 1 = 6 m³

And, 6 m³ = 6000 litres

Hence, the water tank can hold 6000 litres of water.

Question 10. How many planks each of which is 3 m long, 15 cm broad and 5 cm thick can be prepared from a wooden block 6 m long, 75 cm broad and 45 cm thick? 

Solution:

Given, length of wooden block = 6 m

The breadth of wooden block = 75 cm = 0.75 m

The thickness/height of wooden block = 45 cm = 0.45 m

So, the volume of wooden block = l × b × h = 6 × 0.75 × 0.45

= 2.025 m³

Now, length of plank = 3 m

The breadth of plank = 15 cm = 0.15 m

The thickness/height of plank = 5 cm = 0.05 m

So, the volume of plank = l × b × h = 3 × 0.15 × 0.05

= 0.0225 m³

So, the number of plank that can be prepared from wooden block = volume of wooden block/ volume of plank 

= 2.025/0.0225 = 90 

Hence, 90 planks can be made from the given wooden block