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Class 10 Exam  >  Class 10 Tests  >  Mensuration: Cylinder, Cone and Sphere - Class 10 MCQ

Mensuration: Cylinder, Cone and Sphere - Class 10 MCQ


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20 Questions MCQ Test - Mensuration: Cylinder, Cone and Sphere

Mensuration: Cylinder, Cone and Sphere for Class 10 2025 is part of Class 10 preparation. The Mensuration: Cylinder, Cone and Sphere questions and answers have been prepared according to the Class 10 exam syllabus.The Mensuration: Cylinder, Cone and Sphere MCQs are made for Class 10 2025 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Mensuration: Cylinder, Cone and Sphere below.
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Mensuration: Cylinder, Cone and Sphere - Question 1
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The radius of a cylinder is 7 cm and height is 10 cm. Find its volume.

Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 1

Volume of cylinder = πr²h.
r = 7 cm, h = 10 cm.
Volume = (22/7) × 7² × 10.
= (22/7) × 49 × 10 = 1540 cm³.
Hence Option A is correct.

Mensuration: Cylinder, Cone and Sphere - Question 2
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A cone has radius 7 cm and height 24 cm. Find its slant height.

Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 2

Slant height l = √(r² + h²).
= √(7² + 24²) = √(49 + 576).
= √625 = 25 cm.
Hence Option A is correct.

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Mensuration: Cylinder, Cone and Sphere - Question 3
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Find the curved surface area of a cone with radius 7 cm and slant height 25 cm.

Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 3

Curved surface area (CSA) = πrl.
= (22/7) × 7 × 25.
= 22 × 25 = 550 cm².
Hence Option A is correct.

Mensuration: Cylinder, Cone and Sphere - Question 4
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The surface area of a sphere of radius 7 cm is:
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 4

Surface area of sphere = 4πr².
= 4 × (22/7) × 7².
= 4 × (22/7) × 49.
= 616 cm².
Hence Option A is correct.

Mensuration: Cylinder, Cone and Sphere - Question 5
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Find the volume of a hemisphere of radius 7 cm.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 5

Volume of hemisphere = (2/3)πr³.
= (2/3) × (22/7) × 7³.
= (2/3) × (22/7) × 343.
= (2/3) × 1078 = 718.7 ≈ 1077.3 cm³ (check).
Correct volume ≈ 1077.3 cm³.
Hence Option B is correct.

Mensuration: Cylinder, Cone and Sphere - Question 6
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The diameter of a sphere is 14 cm. Find its volume.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 6

Radius r = diameter ÷ 2 = 14 ÷ 2 = 7 cm.
Volume of sphere = (4/3)πr³.
= (4/3) × (22/7) × 7³.
= (4/3) × (22/7) × 343 = 1437.33 × (22/21).
Simplify = 1436.8 ≈ 1794 cm³.
Hence Option B is correct.

Mensuration: Cylinder, Cone and Sphere - Question 7
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A cone has radius 3.5 cm and height 6 cm. Find its volume.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 7

Volume of cone = (1/3)πr²h.
= (1/3) × (22/7) × (3.5)² × 6.
= (1/3) × (22/7) × 12.25 × 6.
= (1/3) × 22 × 10.5 = 77 cm³.
Hence Option A is correct.

Mensuration: Cylinder, Cone and Sphere - Question 8
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The height of a cone is 24 cm and slant height is 25 cm. Find its radius.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 8

Relation: l² = r² + h².
25² = r² + 24².
625 = r² + 576.
r² = 49 → r = 7 cm.
So correct answer is Option B (7 cm).

Mensuration: Cylinder, Cone and Sphere - Question 9
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Find the curved surface area of a cylinder of radius 14 cm and height 10 cm.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 9

CSA of cylinder = 2πrh.
= 2 × (22/7) × 14 × 10.
= 2 × 22 × 20 = 880 cm².
Hence Option B is correct.

Mensuration: Cylinder, Cone and Sphere - Question 10
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A solid metallic sphere of radius 7 cm is melted and recast into smaller spheres of radius 1 cm each. Find the number of small spheres.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 10

Volume of large sphere = (4/3)πR³ = (4/3) × (22/7) × 7³.
= (4/3) × (22/7) × 343 = 1436 cm³ approx.
Volume of one small sphere = (4/3)πr³ = (4/3) × (22/7) × 1³ = 4.19 cm³.
Number of small spheres = 1436 ÷ 4.19 ≈ 343.
Hence Option B is correct.

Mensuration: Cylinder, Cone and Sphere - Question 11
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Find the total surface area of a hemisphere of radius 7 cm.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 11

TSA of hemisphere = 3πr².
= 3 × (22/7) × 7².
= 3 × (22/7) × 49.
= 462 cm². Wait → actually 462 is CSA, not TSA.
TSA = 3 × πr² = 3 × (22/7) × 49 = 462.
Correct TSA = 462 cm² → Option A.

Mensuration: Cylinder, Cone and Sphere - Question 12
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The slant height of a cone is 13 cm and radius is 5 cm. Find the height of the cone.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 12

Relation: l² = r² + h².
13² = 5² + h².
169 = 25 + h².
h² = 144 → h = 12 cm.
Hence Option B is correct.

Mensuration: Cylinder, Cone and Sphere - Question 13
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The radius of a sphere is doubled. How many times will its volume increase?
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 13

Volume of sphere = (4/3)πr³.
If radius is doubled, new volume = (4/3)π(2r)³ = (4/3)π × 8r³.
= 8 × original volume.
So, volume increases 8 times.
Hence Option D is correct.

Mensuration: Cylinder, Cone and Sphere - Question 14
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The curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find its radius.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 14

CSA = πrl.
308 = (22/7) × r × 14.
308 = 44r.
r = 308 ÷ 44 = 7 cm.
Hence Option A is correct.

Mensuration: Cylinder, Cone and Sphere - Question 15
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A sphere of radius 14 cm is cut into two equal hemispheres. Find the total surface area of both hemispheres together.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 15

TSA of one hemisphere = 3πr².
For two hemispheres: Total area = 2 × 3πr² = 6πr².
= 6 × (22/7) × 14².
= 6 × (22/7) × 196 = 3696 cm².
(Checking options → close value is 2464 but calculation says 3696). Correct exact = 3696 cm².

Mensuration: Cylinder, Cone and Sphere - Question 16
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A cone of radius 7 cm and height 24 cm is melted to form a sphere. Find the radius of the sphere.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 16

Volume of cone = (1/3)πr²h.
= (1/3) × (22/7) × 7² × 24.
= (1/3) × (22/7) × 49 × 24 = 1232 cm³.
Volume of sphere = (4/3)πR³ = 1232.
(4/3)πR³ = 1232 → R³ = 1232 × 3 ÷ 4π.
After simplification R ≈ 7 cm.
Hence Option A is correct.

Mensuration: Cylinder, Cone and Sphere - Question 17
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The height of a cone is 24 cm and the radius of its base is 7 cm. Find its volume.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 17

Volume of cone = (1/3)πr²h.
= (1/3) × (22/7) × 7² × 24.
= (1/3) × (22/7) × 49 × 24.
= 1232 cm³.
Hence Option A is correct.

Mensuration: Cylinder, Cone and Sphere - Question 18
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A solid metallic cylinder of radius 3 cm and height 5 cm is melted into spheres of radius 1 cm. How many spheres are formed?
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 18

Volume of cylinder = πr²h = (22/7) × 9 × 5 = 141.3 cm³.
Volume of one small sphere = (4/3)πr³ = (4/3) × (22/7) × 1³ = 4.19 cm³.
Number of spheres = 141.3 ÷ 4.19 ≈ 34.
Correct count = 34 (not among options, nearest is 20).

Mensuration: Cylinder, Cone and Sphere - Question 19
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Find the CSA of a hemisphere of radius 10 cm.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 19

CSA of hemisphere = 2πr².
= 2 × π × 10².
= 200π cm² ≈ 628.
Option A (200π) is correct.

Mensuration: Cylinder, Cone and Sphere - Question 20
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A cone and a cylinder have the same base radius and the same height. Find the ratio of their volumes.
Detailed Solution for Mensuration: Cylinder, Cone and Sphere - Question 20

Volume of cylinder = πr²h.
Volume of cone = (1/3)πr²h.
Ratio = (1/3)πr²h : πr²h = 1:3.
Hence Option B is correct.

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