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Surface Areas and Volumes Practice Questions

Class 10 · Mathematics · 963 free MCQs with instant results and detailed explanations.

963
Total
392
Easy
442
Medium
129
Hard

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Topics in Surface Areas and Volumes

Conversion of Solids 360
Combination of Solids 285
Frustum of a Cone 318

Sample Questions from Surface Areas and Volumes

Here are 10 sample questions. Start a quiz to get randomized questions with scoring.

Q1
Easy
What is the total surface area of a cylinder with a radius of 7 cm and a height of 10 cm?
A. 754 cm²
B. 440 cm²
C. 154 cm²
D. 220 cm²
Show Answer & Explanation
Correct Answer: A
The total surface area of a cylinder is given by 2πr(h + r), where r is the radius and h is the height. Plugging in the values gives 2π(7)(10 + 7) = 754 cm².
Q2
Easy
What is the total surface area of a sphere with a radius of 6 cm?
A. 144π cm²
B. 36π cm²
C. 72π cm²
D. 24π cm²
Show Answer & Explanation
Correct Answer: A
The total surface area of a sphere is given by 4πr². For r = 6 cm, it is 4π(6)² = 144π cm².
Q3
Easy
A cylinder has a height of 10 cm and a radius of 4 cm. What is its lateral surface area?
A. 80π cm²
B. 60π cm²
C. 40π cm²
D. 100π cm²
Show Answer & Explanation
Correct Answer: A
Lateral surface area of a cylinder = 2πrh. Here, it is 2π(4)(10) = 80π cm².
Q4
Medium
A cylindrical tank with radius 2 m and height 5 m is filled with water. If a spherical ball of radius 0.5 m is submerged in the tank, what is the volume of water displaced?
A. 0.5 m³
B. 0.3 m³
C. 0.2 m³
D. 0.1 m³
Show Answer & Explanation
Correct Answer: A
The volume of water displaced by the submerged ball is equal to the volume of the ball: V = (4/3)πr³ = (4/3)π(0.5)³ = 0.5 m³.
Q5
Medium
If the radius of a cylinder is doubled while keeping the height the same, how does its volume change?
A. Remains the same
B. Doubles
C. Triples
D. Quadruples
Show Answer & Explanation
Correct Answer: D
Volume of cylinder = πr²h. When radius is doubled, new volume = π(2r)²h = 4πr²h, which is four times the original volume.
Q6
Medium
A hemisphere is placed on top of a cylinder. If the radius of both shapes is 5 cm and the height of the cylinder is 12 cm, what is the total height of the combined solid?
A. 15 cm
B. 17 cm
C. 12 cm
D. 10 cm
Show Answer & Explanation
Correct Answer: B
The total height is the sum of the height of the cylinder and the radius of the hemisphere.
Q7
Medium
If a cube of side 'a' cm is melted and recast into a cylinder of radius 'r' cm and height 'h' cm, what is the relationship between 'a', 'r', and 'h'?
A. a³ = πr²h
B. a² = πr²h
C. a = πr²h
D. a³ = 2πr²h
Show Answer & Explanation
Correct Answer: A
The volume of the cube must equal the volume of the cylinder after recasting.
Q8
Hard
A cone and a cylinder have the same base radius and height. If the radius is r and the height is h, what is the ratio of their volumes?
A. 1:3
B. 1:2
C. 3:1
D. 2:1
Show Answer & Explanation
Correct Answer: A
The volume of a cone is (1/3)πr²h and for a cylinder, it is πr²h. Thus, the ratio is 1:3.
Q9
Hard
Find the lateral surface area of a right circular cone with a radius of 5 cm and a height of 12 cm.
A. 65π cm²
B. 40π cm²
C. 60π cm²
D. 50π cm²
Show Answer & Explanation
Correct Answer: A
The lateral surface area of a cone is given by πrl, where l is the slant height calculated from radius and height.
Q10
Hard
What is the volume of a cylinder with a height of 10 cm and a radius of 5 cm?
A. 250π cm³
B. 200π cm³
C. 150π cm³
D. 100π cm³
Show Answer & Explanation
Correct Answer: A
The volume of a cylinder is calculated using the formula V = πr²h.

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Surface Areas and Volumes — Class 10 Mathematics Practice Questions Online

This page contains 963 practice MCQs for the chapter Surface Areas and Volumes in Class 10 Mathematics. The questions are organized by difficulty — 392 easy, 442 medium, 129 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit. This chapter covers 3 topics, giving you comprehensive coverage of the entire chapter.