Maths · Mensuration · chapter 12 of 14

Class 10 Maths Chapter 12: Surface Areas and Volumes MCQs with answers

10 multiple-choice questions on Surface Areas and Volumes, each with its answer and the reason, written from the NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
A cylindrical pillar has radius 7 cm and height 10 cm. Take π = 22/7. Its curved surface area is
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Answer: (a) 440 cm²

CSA = 2πrh = 2 × (22/7) × 7 × 10 = 440 cm².

Question 2
The curved surface area of a hemisphere of radius 14 cm is (Take π = 22/7)
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Answer: (c) 1232 cm²

CSA of a hemisphere = 2πr² = 2 × (22/7) × 196 = 1232 cm². 2464 cm² is the whole sphere; 1848 cm² adds the flat face.

Question 3
A solid cone has base radius 3 cm and height 7 cm. Take π = 22/7. Its volume is
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Answer: (b) 66 cm³

V = (1/3)πr²h = (1/3) × (22/7) × 9 × 7 = 66 cm³. 198 cm³ forgets the 1/3.

Question 4
The volume of a solid hemisphere of radius 21 cm is (Take π = 22/7)
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Answer: (d) 19404 cm³

V = (2/3)πr³ = (2/3) × (22/7) × 9261 = 19404 cm³. 38808 cm³ is the full sphere; 2772 cm² is the curved surface, not a volume.

Question 5
A cone has base radius 6 cm and height 8 cm. Take π = 3.14. Its curved surface area is
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Answer: (a) 188.4 cm²

l = √(6² + 8²) = 10 cm. CSA = πrl = 3.14 × 6 × 10 = 188.4 cm². Using the height for l gives 150.72 cm²; adding the base gives 301.44 cm².

Question 6
In this chapter, the curved surface area (CSA) of a solid means
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Answer: (b) the area of its curved surface only

CSA is Curved Surface Area: only the curved part. The area of all faces is the TSA, and the space enclosed is the volume.

Question 7
Asha works out the paint needed to cover a toy and writes her answer as 550 cm³. What does the unit tell you?
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Answer: (c) She has found a volume, but paint covers a surface, so the answer must be in cm².

cm³ belongs to volume and cm² to surface area. Paint covers a surface, so the unit shows a volume formula was used by mistake.

Question 8
A toy is made by fixing a cone on a hemisphere so that the join is smooth. The base radius of the cone must be
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Answer: (d) equal to the radius of the hemisphere

For a smooth join the cone's base must exactly cover the hemisphere's flat face, so the two radii are equal.

Question 9
A hemisphere is fixed on one face of a cube of edge 10 cm. The greatest radius the hemisphere can have is
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Answer: (a) 5 cm

The hemisphere's diameter can be at most the cube's edge, 10 cm, so its radius is at most 5 cm.

Question 10
A solid is a cylinder of radius r and height h with a hemisphere of radius r fixed at each end. Its total surface area is
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Answer: (b) πr(2h + 4r)

TSA = CSA of cylinder + CSA of two hemispheres = 2πrh + 2(2πr²) = πr(2h + 4r). The flat ends are covered, so they are not counted.

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