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 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 1st cube be a cm and side of the 2nd cube be 2a cm.
Volume of the 1st cube = a3
Volume of the 2nd 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 1st cube be a cm and side of the 2nd cube be 2a cm.
Total surface area of the 1st cube = 6a2
Total surface of the 2nd 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
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