CBSE Class 10 Mathematics Surface Areas and Volumes MCQs Set 23

Multiple Choice Questions (MCQs) for Class 10 Mathematics: Chapter 12 Surface Areas and Volumes

Review structured MCQ sets for Class 10 Mathematics Chapter 12 Surface Areas and Volumes. Built according to official CBSE guidelines, these downloadable questions support daily revision and core concept reinforcement.

Practice Chapter 12 Surface Areas and Volumes MCQs for Class 10 Mathematics

Navigate directly to the 50 objective questions for Chapter 12 Surface Areas and Volumes using the digital viewer below. Each practice set includes verified answer keys, allowing students to instantly cross-check their work and identify areas requiring further revision.

Multiple Choice Questions

Question 1: The length of canvas, 2 m wide, required to make a conical tent 20 m in diameter and 42 m in slant height, allowing 10% extra for folds and stitching (use π = 22/7), is:
(a) 660 m
(b) 792 m
(c) 1320 m
(d) 726 m
Show Answer & Explanation

Answer: (d) 726 m

Explanation:
1. Curved surface = π(10)(42) = 1320 m². With 10% extra the area is 1452 m². Length = 1452/2 = 726 m.

Teacher's Note:
1. Curved surface area of a cylinder = 2 pi r h, of a cone = pi r l, of a sphere = 4 pi r^2 and of a hemisphere = 2 pi r^2, where l = square root of (r^2 + h^2).

Question 2: From a cube of edge 14 cm, a cone of maximum size is carved out. The volume of the cone (use π = 22/7) is:
(a) 2156.00 cm³
(b) 1437.33 cm³
(c) 718.67 cm³
(d) 539.00 cm³
Show Answer & Explanation

Answer: (c) 718.67 cm³

Explanation:
1. The largest cone has base radius 7 cm and height 14 cm. Volume = (1/3)(22/7)(49)(14) = 2156/3 = 718.67 cm³.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 3: A cone of maximum volume is carved out of a wooden block of size 20 cm x 10 cm x 10 cm. Taking π = 3.1416, its volume is:
(a) 392.7 cm³
(b) 654.5 cm³
(c) 523.6 cm³
(d) 1047.2 cm³
Show Answer & Explanation

Answer: (c) 523.6 cm³

Explanation:
1. The largest cone has base radius 5 cm and height 20 cm. Volume = (1/3)(3.1416)(25)(20) = 523.6 cm³.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 4: A pen stand is a cuboid 15 cm x 10 cm x 3.5 cm with four conical depressions each of radius 0.5 cm and depth 1.4 cm. The volume of wood in the stand (use π = 22/7) is:
(a) 526.47 cm³
(b) 523.53 cm³
(c) 521.07 cm³
(d) 500.00 cm³
Show Answer & Explanation

Answer: (b) 523.53 cm³

Explanation:
1. Cuboid = 15 x 10 x 3.5 = 525 cm³. Each depression = (1/3)(22/7)(0.25)(1.4) = 0.3667 cm³, four give 1.4667 cm³. Wood = 525 - 1.47 = 523.53 cm³.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 5: From a solid cylinder of height 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and diameter is hollowed out. The total surface area of the remaining solid, to the nearest cm² (use π = 22/7), is:
(a) 18 cm²
(b) 15 cm²
(c) 20 cm²
(d) 22 cm²
Show Answer & Explanation

Answer: (a) 18 cm²

Explanation:
1. Slant height of the cone = √(0.49 + 5.76) = 2.5 cm. Surface = cylinder CSA 2π(0.7)(2.4) + one base π(0.49) + cone CSA π(0.7)(2.5) = (3.36 + 0.49 + 1.75)π = 5.6π = 17.6, about 18 cm².

Teacher's Note:
1. Curved surface area of a cylinder = 2 pi r h, of a cone = pi r l, of a sphere = 4 pi r^2 and of a hemisphere = 2 pi r^2, where l = square root of (r^2 + h^2).

Question 6: From a solid cylinder of height 8 cm and radius 6 cm, a conical cavity of height 8 cm and base radius 6 cm is hollowed out. The volume of the remaining solid (use π = 3.1416) is:
(a) 301.6 cm³
(b) 452.4 cm³
(c) 904.8 cm³
(d) 603.2 cm³
Show Answer & Explanation

Answer: (d) 603.2 cm³

Explanation:
1. Volume = (2/3)πr²h = (2/3)π(36)(8) = 192π = 603.2 cm³.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 7: A metallic cylinder of radius 3 cm and height 5 cm has a conical hole of radius 3/2 cm and depth 8/9 cm drilled and filled with a lighter metal B. The ratio of the volume of metal A to the volume of metal B is:
(a) 131 : 2
(b) 133 : 4
(c) 45 : 2
(d) 133 : 2
Show Answer & Explanation

Answer: (d) 133 : 2

Explanation:
1. Volume of the cylinder = 45π. Cone = (1/3)π(9/4)(8/9) = 2π/3. Metal A = 45π - 2π/3 = 133π/3. Ratio A : B = (133/3) : (2/3) = 133 : 2.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 8: An open cylindrical vessel of internal diameter 7 cm and height 8 cm stands on a table. A solid metallic right circular cone of base diameter 7/2 cm and height 8 cm is placed inside. The volume of water needed to fill the vessel (use π = 22/7) is:
(a) 308.00 cm³
(b) 264.00 cm³
(c) 282.33 cm³
(d) 333.67 cm³
Show Answer & Explanation

Answer: (c) 282.33 cm³

Explanation:
1. Vessel volume = (22/7)(12.25)(8) = 308 cm³. Cone volume = (1/3)(22/7)(3.0625)(8) = 25.67 cm³. Water needed = 308 - 25.67 = 282.33 cm³ (282 1/3).

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 9: A hemispherical tank 3 m in diameter is full of water and is emptied by a pipe at the rate of 3 4/7 litres per second. The time taken to empty half the tank (use π = 22/7) is:
(a) 8.3 minutes
(b) 16.5 minutes
(c) 33.0 minutes
(d) 12.4 minutes
Show Answer & Explanation

Answer: (b) 16.5 minutes

Explanation:
1. Half the volume = (1/2)(2/3)π(1.5)³ = 1.125π = 3.5357 m³ = 3535.7 litres. Rate = 25/7 litres per second, so time = 3535.7 x 7/25 = 990 s = 16.5 minutes.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 10: A cone has the same volume as a cylinder of height 9 cm and diameter 40 cm. If the height of the cone is 108 cm, the radius of its base is:
(a) 10 cm
(b) 5 cm
(c) 15 cm
(d) 20 cm
Show Answer & Explanation

Answer: (a) 10 cm

Explanation:
1. Cylinder = π(20)²(9) = 3600π. For the cone (1/3)πr²(108) = 36πr² = 3600π, so r = 10 cm.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 11: The entire surface of a solid cone of base radius 3 cm and height 4 cm equals the entire surface of a solid right circular cylinder of diameter 4 cm. The ratio of their curved surfaces and the ratio of their volumes are respectively:
(a) 15 : 16 and 3 : 4
(b) 15 : 16 and 4 : 3
(c) 16 : 15 and 3 : 4
(d) 5 : 6 and 3 : 4
Show Answer & Explanation

Answer: (a) 15 : 16 and 3 : 4

Explanation:
1. Cone slant height = 5, total surface = π(3)(5) + π(9) = 24π. Cylinder with r = 2: 2π(2)(h + 2) = 24π gives h = 4. Curved surfaces: 15π : 16π = 15 : 16. Volumes: (1/3)π(9)(4) = 12π and π(4)(4) = 16π, ratio 3 : 4.

Teacher's Note:
1. Curved surface area of a cylinder = 2 pi r h, of a cone = pi r l, of a sphere = 4 pi r^2 and of a hemisphere = 2 pi r^2, where l = square root of (r^2 + h^2).

Question 12: A girl fills a cylindrical bucket 32 cm high and 18 cm in radius with sand and empties it on the ground to make a conical heap 24 cm high. The slant height of the heap is:
(a) \( 12\sqrt{15} \) cm
(b) \( 6\sqrt{13} \) cm
(c) \( 36 \) cm
(d) \( 12\sqrt{13} \) cm
Show Answer & Explanation

Answer: (d) \( 12\sqrt{13} \) cm

Explanation:
1. Volume of sand = π(324)(32) = 10368π. For the heap (1/3)πr²(24) = 8πr² = 10368π gives r² = 1296 and r = 36. Slant height = √(1296 + 576) = √1872 = 12√13 cm.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 13: A hollow metallic cylindrical tube has internal radius 3 cm and height 21 cm and the metal is 1/2 cm thick. It is melted and cast into a right circular cone of height 7 cm. The radius of the cone, to one decimal place, is:
(a) 4.8 cm
(b) 6.0 cm
(c) 5.4 cm
(d) 7.2 cm
Show Answer & Explanation

Answer: (c) 5.4 cm

Explanation:
1. External radius = 3.5 cm. Metal volume = π(12.25 - 9)(21) = 68.25π. For the cone (1/3)πr²(7) = 68.25π gives r² = 29.25, so r = 5.4 cm.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 14: A right circular cone of height 20 cm and base diameter 30 cm is cast into smaller cones of equal size, each with base radius 10 cm and height 9 cm. The number of cones made is:
(a) 4
(b) 5
(c) 6
(d) 10
Show Answer & Explanation

Answer: (b) 5

Explanation:
1. Large cone = (1/3)π(225)(20) = 1500π. Small cone = (1/3)π(100)(9) = 300π. Number = 5.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 15: The largest sphere is carved out of a cube of side 7 cm. Its volume (use π = 22/7) is:
(a) 343.00 cm³
(b) 179.67 cm³
(c) 89.83 cm³
(d) 269.50 cm³
Show Answer & Explanation

Answer: (b) 179.67 cm³

Explanation:
1. The diameter equals the edge, so r = 3.5 cm. Volume = (4/3)(22/7)(42.875) = 179.67 cm³ (179 2/3).

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 16: A hemispherical bowl of internal radius 3.5 cm is full of water. Its contents are emptied into a cylindrical vessel of internal radius 7 cm. The height of water in the cylinder is:
(a) 0.58 cm
(b) 1.17 cm
(c) 0.29 cm
(d) 1.75 cm
Show Answer & Explanation

Answer: (a) 0.58 cm

Explanation:
1. Volume of water = (2/3)π(3.5)³ = (2/3)π(42.875). Height = [(2/3)(42.875)]/49 = 0.5833 = 7/12 cm.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 17: An iron pillar is a cylinder of radius 8 cm and height 240 cm with a cone of height 36 cm of the same radius on top. If 1 cm³ of iron weighs 7.8 g, the weight of the pillar (use π = 22/7) is:
(a) 263.58 kg
(b) 527.15 kg
(c) 790.73 kg
(d) 395.37 kg
Show Answer & Explanation

Answer: (d) 395.37 kg

Explanation:
1. Volume = π(64)(240) + (1/3)π(64)(36) = π(15360 + 768) = 16128π = 50688 cm³. Weight = 50688 x 7.8 g = 395366.4 g = 395.37 kg.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 18: A hemispherical bowl of internal diameter 36 cm contains liquid to be filled in cylindrical bottles of radius 3 cm and height 6 cm. The number of bottles required is:
(a) 36
(b) 64
(c) 72
(d) 108
Show Answer & Explanation

Answer: (c) 72

Explanation:
1. Bowl volume = (2/3)π(18)³ = 3888π. Bottle volume = π(9)(6) = 54π. Number = 72.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 19: Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. The number of marbles that must be dropped so that the water level rises by 5.6 cm is:
(a) 75
(b) 125
(c) 150
(d) 200
Show Answer & Explanation

Answer: (c) 150

Explanation:
1. Rise volume = π(3.5)²(5.6) = 68.6π. Marble = (4/3)π(0.7)³ = 0.45733π. Number = 68.6/0.45733 = 150.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 20: The curved surface area of a right circular cone is 12320 cm² and the radius of its base is 56 cm (use π = 22/7). Its height is:
(a) 28 cm
(b) 42 cm
(c) 49 cm
(d) 56 cm
Show Answer & Explanation

Answer: (b) 42 cm

Explanation:
1. Slant height l = 12320/(π x 56) = 70 cm. Height = √(70² - 56²) = √(4900 - 3136) = √1764 = 42 cm.

Teacher's Note:
1. Curved surface area of a cylinder = 2 pi r h, of a cone = pi r l, of a sphere = 4 pi r^2 and of a hemisphere = 2 pi r^2, where l = square root of (r^2 + h^2).

Question 21: The volume of a right circular cylindrical vessel is 448π cm³ and its height is 7 cm. The radius of its base is:
(a) 8 cm
(b) 6 cm
(c) 7 cm
(d) 9 cm
Show Answer & Explanation

Answer: (a) 8 cm

Explanation:
1. πr²(7) = 448π gives r² = 64 and r = 8 cm.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

Question 22: A building is a cylinder surmounted by a hemispherical dome and contains 41 19/21 m³ of air. If the internal diameter of the building equals its total height above the floor, its height is:
(a) 2 m
(b) 3 m
(c) 6 m
(d) 4 m
Show Answer & Explanation

Answer: (d) 4 m

Explanation:
1. 41 19/21 = 880/21. With radius r the total height is 2r, so the cylinder height is r. Volume = πr³ + (2/3)πr³ = (5/3)(22/7)r³ = 880/21, so r³ = 8, r = 2 m and the height is 4 m.

Teacher's Note:
1. Volume of a cuboid = l x b x h, of a cube = a^3, of a cylinder = pi r^2 h, of a cone = (1/3) pi r^2 h, of a sphere = (4/3) pi r^3 and of a hemisphere = (2/3) pi r^3.
2. When a solid is melted and recast, its volume stays the same.

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Practice MCQs for Class 10 Mathematics Chapter 12 Surface Areas and Volumes

Download Multiple Choice Questions: Chapter 12 Surface Areas and Volumes (Class 10 Mathematics)

Review structured objective questions for Class 10 Mathematics Chapter 12 Surface Areas and Volumes. Built according to official CBSE guidelines, these MCQ sets support daily revision and core concept reinforcement.

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