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 cm². Its volume is

Ans: (b) 125 cm³

(3) The volume of a cube is 343 cm³. Its total surface area is

Ans: (c) 294 cm²

(4) The cost of painting the whole surface area of a cube at the rate of 10 paise per cm² is Rs 264.60. Then, the volume of the cube is

Ans: (b) 9261 cm³

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

Surface area = 2646 cm²

Let the surface area of a cube be 6a² cm²

(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 cm³

Volume of the box = (100 cm)³ = 1000000 cm³

(7) The edge of a cuboid are in the ratio 1 : 2 : 3 and its surface area is 88 cm². The volume of the cuboid is

Ans: (a) 48 cm³

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

Surface area = {2(a×2a + 2a× 3a + 3a × a)} cm²

= 2 (2a² + 6a² + 3a²) cm² = (2 × 11a²) cm² = 22a² cm²

Volume of the cuboid = {2 ×(2×2) × (3×2)} cm³

= (2 × 4 × 6) cm³ = 48 cm³

(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 cm²

Solution: Surface area = {2(10×4) + (4×3) + (3× 10)} cm²

= {2 × (40 + 12 + 30)} cm² = (2 × 82) cm² = 164 cm²

(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) m³ = 0.72 m³

Given 1 m³ = 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 m³ [∵ 1m³ = 1000 L]

Then, volume of the reservoir = (6 × 3.5 × x) m³

∴ 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 m³ of space?

Ans: (b) 88

Solution: Volume of the room = (10 × 8 × 3.3) m³ = 264 m³

(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) m³ = 30 m³

We know, 1 m³ = 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 cm²

Solution: Total surface area of cardboard,

= {2 × (25 × 15 + 15 × 8 + 8 × 25)} cm²

= {2 × (375 + 120 + 200)} cm²

= 1390 cm²

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

Ans: (d) 64 cm³

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

∴ a = 4

Then, volume = a³ = (4 × 4 × 4) cm³ = 64 cm³

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

Ans: (b) 486 cm²

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

∴ a = 9

Then, total surface area = 6a² = (6 × 9 × 9) cm² = 486 cm²

(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 = a³

Volume of the 2^nd cube = (2a)³ = 8a³

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 = 6a²

Total surface of the 2^nd cube = 6(2a)² = 24a²

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} cm³

= (216 + 512 + 1000) cm³ = 1728 cm³

(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 cm³

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) cm³ = 625 cm³

(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 m³

Solution: Here, Diameter = 2 m

Radius = 1 m

(22) If the capacity of a cylindrical tank is 1848 m³ 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 cm³ 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 cm³

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 cm²

(28) The height of a cylinder is 14 cm and its curved surface area is 264 cm². The volume of the cylinder is

Ans: (b) 396 cm³

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 cm². The volume of the cylinder is

Ans: (a) 770 cm³

Solution: Here, radius = 7 cm

Let the height be h cm.

∴ Curved surface area = 2 cm²

(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