# RS Aggarwal Class 8 Math Twentieth Chapter Volume and Surface Area of Solids Exercise 20C Solution

## EXERCISE 20C

### OBJECTIVE QUESTIONS

#### Tick (√) the correct answer in each of the following:

**(1) The maximum length of a pencil that can be kept in a rectangular box of dimensions 12 cm ****× 9 cm × 8 cm, is**

Ans: (b) 17 cm

**(2) The total surface area of a cube is 150 cm ^{2}. Its volume is**

Ans: (b) 125 cm^{3}

**(3) The volume of a cube is 343 cm ^{3}. Its total surface area is**

Ans: (c) 294 cm^{2}

**(4) The cost of painting the whole surface area of a cube at the rate of 10 paise per cm ^{2} is Rs 264.60. Then, the volume of the cube is**

Ans: (b) 9261 cm^{3}

Solution: Total cost = Rs (264.60 × 10) = Rs 2646

Surface area = 2646 cm^{2}

Let the surface area of a cube be 6a^{2} cm^{2}

**(5) How many bricks, each measuring 25 cm ****× 11.25 cm × 6 cm, will be needed to build a wall 8 m long, 6 m high and 22.5 cm thick?**

Ans: (c) 6400

**(6) How many cubes of 10 cm edge can be put in a cubical box of 1 m edge?**

Ans: (c) 1000

Solution: Volume of each small cube = (10 cm)^{3} = 1000 cm^{3}

Volume of the box = (100 cm)^{3} = 1000000 cm^{3}

**(7) The edge of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm ^{2}. The volume of the cuboid is**

Ans: (a) 48 cm^{3}

Solution: Let the length of the edges a cm, 2a cm and 3a cm.

Surface area = {2(a×2a + 2a× 3a + 3a × a)} cm^{2}

= 2 (2a^{2} + 6a^{2} + 3a^{2}) cm^{2} = (2 × 11a^{2}) cm^{2} = 22a^{2} cm^{2}

Volume of the cuboid = {2 ×(2×2) × (3×2)} cm^{3}

= (2 × 4 × 6) cm^{3} = 48 cm^{3}

**(8) Two cubes have their volumes in the ratio 1 : 27. The ratio of their surface areas is **

Ans: (b) 1 : 9

∴ Ratio of the surface areas = 1 : 9

**(9) The surface area of a (10 cm × 4 cm × 3 cm) brick is**

Ans: (c) 164 cm^{2}

Solution: Surface area = {2(10×4) + (4×3) + (3× 10)} cm^{2}

= {2 × (40 + 12 + 30)} cm^{2} = (2 × 82) cm^{2} = 164 cm^{2}

**(10) An iron beam is 9 m long, 40 cm wide and 20 cm high. If 1 cubic metre of iron weighs 50 kg, what is the weight of the beam?**

Ans: (c) 36 kg

Solution: Here 40 cm = 0.4 m; 20 cm = 0.2 m

Volume of the iron beam = (9 × 0.4 × 0.2) m^{3} = 0.72 m^{3}

Given 1 m^{3} = 50 kg

Then weight of the beam = (0.72 × 50) kg = 36 kg

**(11) A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and its breadth is 3.5 m, the depth of the reservoir is**

Ans: (a) 2 m

Solution: Let the depth of the water be x cm.

42000 L = 42 m^{3} [∵ 1m^{3} = 1000 L]

Then, volume of the reservoir = (6 × 3.5 × x) m^{3}

∴ 6 × 3.5 × x = 42

⇒ 21 x = 42

⇒ x = 2 m

**(12) The dimensions of a room are (10 m × 8 m × 3.3 m). How many men can be accommodated in this room if each man requires 3 m ^{3} of space?**

Ans: (b) 88

Solution: Volume of the room = (10 × 8 × 3.3) m^{3} = 264 m^{3}

**(13) A rectangular water tank is 3 m long, 2 m wide and 5 m high. How many litres of water can it hold?**

Ans: (a) 30000

Solution: Volume of the tank = (3 × 2 × 5) m^{3} = 30 m^{3}

We know, 1 m^{3} = 1000 L

∴ Quantity of water = (30 × 1000) L = 30000 L.

**(14) The area of the cardboard needed to make a box of size 25 cm × 15 cm × 8 cm will be **

Ans: (b) 1390 cm^{2}

Solution: Total surface area of cardboard,

= {2 × (25 × 15 + 15 × 8 + 8 × 25)} cm^{2}

= {2 × (375 + 120 + 200)} cm^{2}

= 1390 cm^{2}

**(15) The diagonal of a cube is 4√3 cm long. Its volume is**

Ans: (d) 64 cm^{3}

Solution: Diagonal of a cube = a√3 = 4√3

∴ a = 4

Then, volume = a^{3} = (4 × 4 × 4) cm^{3} = 64 cm^{3}

**(16) The diagonal of a cube is 9√3 cm long. Its total surface area is**

Ans: (b) 486 cm^{2}

Solution: Diagonal of a cube = √3 a = 9 √3

∴ a = 9

Then, total surface area = 6a^{2} = (6 × 9 × 9) cm^{2} = 486 cm^{2}

**(17) If each side of a cube is doubled then its volume**

Ans: (d) becomes 8 times

Solution: Let the side of 1^{st} cube be a cm and side of the 2^{nd} cube be 2a cm.

Volume of the 1^{st} cube = a^{3}

Volume of the 2^{nd} cube = (2a)^{3} = 8a^{3}

Then, the volume becomes 8 times the original volume.

**(18) If each side of a cube is doubled, its surface area**

Ans: (b) Becomes 4 times

Solution: Let the side of 1^{st} cube be a cm and side of the 2^{nd} cube be 2a cm.

Total surface area of the 1^{st} cube = 6a^{2}

Total surface of the 2^{nd} cube = 6(2a)^{2} = 24a^{2}

Then, the surface area becomes 4 times the original surface area.

**(19) Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is**

Ans: (a) 12 cm

Total volume of three cubes = {(6)^{3} + (8)^{3} + (10)^{3}} cm^{3}

= (216 + 512 + 1000) cm^{3} = 1728 cm^{3}

**(20) Five equal cubes, each of edge 5 cm, are placed adjacent to each other. The volume of the cuboid so formed, is**

Ans: (d) 625 cm^{3}

Solution: Length of the cube = (5+5+5+5+5) = 25 cm

Breadth = 5 cm

Height = 5 cm

∴ Volume of the cuboid = (25 × 5 × 5) cm^{3} = 625 cm^{3}

**(21) A circular well with a diameter of 2 metres, is dug to a depth of 14 metres. What is the volume of the earth dug out?**

Ans: (d) 44 m^{3}

Solution: Here, Diameter = 2 m

Radius = 1 m

**(22) If the capacity of a cylindrical tank is 1848 m ^{3} and the diameter of its base is 14 m, the depth of the tank is**

Ans: (b) 12 m

Solution: Here, Diameter = 14 m

Radius = 7 m

Let the depth be h m.

**(23) The ratio of the total surface area to the lateral surface area of a cylinder whose radius is 20 cm and height 60 cm, is**

Ans: (c) 4 : 3

**(24) The number of coins, each of radius 0.75 cm and thickness 0.2 cm, to be melted to make a right circular cylinder of height 8 cm and base radius 3 cm is**

Ans: (d) 640

**(25) 66 cm ^{3} of silver is drawn into a wire 1 mm in diameter. The length of the wire will be **

Ans: (b) 84 m

Solution: Here, Diameter = 1 mm, r = 0.05 cm

**(26) The height of a cylinder is 14 cm and its diameter is 10 cm. The volume of the cylinder is**

Ans: (a) 1100 cm^{3}

Solution: here, diameter = 10 cm, radius = 5 cm

**(27) The height of a cylinder is 80 cm and the diameter of its base is 7 cm. The whole surface area of the cylinder is**

Ans: (a) 1837 cm^{2}

**(28) The height of a cylinder is 14 cm and its curved surface area is 264 cm ^{2}. The volume of the cylinder is**

Ans: (b) 396 cm^{3}

Solution: Let the radius of the cylinder be r cm.

**(29) The diameter of a cylinder is 14 cm and its curved surface area is 220 cm ^{2}. The volume of the cylinder is**

Ans: (a) 770 cm^{3}

Solution: Here, radius = 7 cm

Let the height be h cm.

∴ Curved surface area = 2 cm^{2}

**(30) The ratio of the radii of two cylinders is 2 : 3 and the ratio of their heights is 5 : 3. The ratio of their volumes will be **

Ans: (c) 20 : 27