Chapter Exam

Chapter 7: Mensuration — Online MCQ Test

Q: The curved surface area of a right circular cylinder of radius r and height h is ______.

Answer: A. 2πrh — The curved surface area of a cylinder is the area of its rectangular curved part, which is 2πrh.

Q: The volume of a right circular cone of radius r and height h is ______.

Answer: B. 1/3 πr²h — A cone has one-third the volume of a cylinder with the same base radius and height, so its volume is 1/3 πr²h.

Q: The total surface area of a sphere of radius r is ______.

Answer: C. 4πr² — The total surface area of a sphere is 4πr².

Q: The curved surface area of a hemisphere of radius r is ______.

Answer: B. 2πr² — A hemisphere is half of a sphere, so its curved surface area is half of 4πr², which is 2πr².

Q: Find the curved surface area of a cylinder of radius 7 cm and height 10 cm. Use π = 22/7.

Answer: B. 440 cm² — CSA = 2πrh = 2 × 22/7 × 7 × 10 = 440 cm².

Q: A cone has radius 3 cm and height 4 cm. What is its curved surface area?

Answer: B. 15π cm² — The slant height is √(3² + 4²) = 5 cm. Hence CSA = πrl = π × 3 × 5 = 15π cm².

Q: A solid capsule is made of a cylinder of radius 3 cm and length 10 cm with two hemispherical ends. Find its total surface area.

Answer: C. 96π cm² — Total surface area = CSA of cylinder + surface area of two hemispheres = 2πrh + 4πr² = 60π + 36π = 96π cm².

Q: A cone is exactly fitted inside a cylinder with the same radius and height. What is the ratio of the volume of the cone to the remaining volume of the cylinder?

Answer: B. 1 : 2 — The cone occupies 1/3 of the cylinder volume, so the remaining part is 2/3. Therefore the ratio is 1 : 2.

Q: A solid is made by joining a cylinder of radius 7 cm and height 10 cm, a hemisphere on one end, and a cone of height 24 cm on the other end, all with the same radius. Find the total outer surface area. Use π = 22/7.

Answer: B. 1298 cm² — Only outer curved surfaces are counted: cylinder CSA = 440, hemisphere CSA = 308, cone CSA = 550. Total = 1298 cm².

Q: A cone is cut by a plane parallel to its base exactly halfway along its height from the vertex. What is the ratio of the volume of the smaller cone to the volume of the frustum?

Answer: B. 1 : 7 — The linear scale factor of the small cone is 1/2, so its volume is 1/8 of the original cone. The frustum volume is 7/8, so the ratio is 1 : 7.

MATHS · CLASS 10th · Tamil Nadu State Board

Practice Chapter 7: Mensuration with a free chapter-wise online MCQ test for Tamil Nadu State Board CLASS 10th MATHS. This chapter covers: Cylinder Cone Sphere Hemisphere Surface area Curved surface area Total surface area Volume Frustum Conversion of solids Composite solids. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 7: Mensuration — Important Questions & Answers (FAQ)

Frequently asked questions from Tamil Nadu State Board CLASS 10th MATHS — Chapter 7: Mensuration, with answers and explanations. These are sample questions; the exam has its own separate question set.

The curved surface area of a right circular cylinder of radius r and height h is ______.

A. 2πrh ✓
B. πr²h
C. 2πr(h + r)
D. πrl

Answer: A. 2πrh
The curved surface area of a cylinder is the area of its rectangular curved part, which is 2πrh.

The volume of a right circular cone of radius r and height h is ______.

A. πr²h
B. 1/3 πr²h ✓
C. 2/3 πr²h
D. πrh

Answer: B. 1/3 πr²h
A cone has one-third the volume of a cylinder with the same base radius and height, so its volume is 1/3 πr²h.

The total surface area of a sphere of radius r is ______.

A. 2πr²
B. 3πr²
C. 4πr² ✓
D. 4/3 πr³

Answer: C. 4πr²
The total surface area of a sphere is 4πr².

The curved surface area of a hemisphere of radius r is ______.

A. πr²
B. 2πr² ✓
C. 3πr²
D. 4πr²

Answer: B. 2πr²
A hemisphere is half of a sphere, so its curved surface area is half of 4πr², which is 2πr².

Find the curved surface area of a cylinder of radius 7 cm and height 10 cm. Use π = 22/7.

A. 220 cm²
B. 440 cm² ✓
C. 880 cm²
D. 154 cm²

Answer: B. 440 cm²
CSA = 2πrh = 2 × 22/7 × 7 × 10 = 440 cm².

A cone has radius 3 cm and height 4 cm. What is its curved surface area?

A. 12π cm²
B. 15π cm² ✓
C. 24π cm²
D. 9π cm²

Answer: B. 15π cm²
The slant height is √(3² + 4²) = 5 cm. Hence CSA = πrl = π × 3 × 5 = 15π cm².

A solid capsule is made of a cylinder of radius 3 cm and length 10 cm with two hemispherical ends. Find its total surface area.

A. 60π cm²
B. 78π cm²
C. 96π cm² ✓
D. 114π cm²

Answer: C. 96π cm²
Total surface area = CSA of cylinder + surface area of two hemispheres = 2πrh + 4πr² = 60π + 36π = 96π cm².

A cone is exactly fitted inside a cylinder with the same radius and height. What is the ratio of the volume of the cone to the remaining volume of the cylinder?

A. 1 : 1
B. 1 : 2 ✓
C. 2 : 1
D. 1 : 3

Answer: B. 1 : 2
The cone occupies 1/3 of the cylinder volume, so the remaining part is 2/3. Therefore the ratio is 1 : 2.

A solid is made by joining a cylinder of radius 7 cm and height 10 cm, a hemisphere on one end, and a cone of height 24 cm on the other end, all with the same radius. Find the total outer surface area. Use π = 22/7.

A. 1144 cm²
B. 1298 cm² ✓
C. 1452 cm²
D. 1606 cm²

Answer: B. 1298 cm²
Only outer curved surfaces are counted: cylinder CSA = 440, hemisphere CSA = 308, cone CSA = 550. Total = 1298 cm².

A cone is cut by a plane parallel to its base exactly halfway along its height from the vertex. What is the ratio of the volume of the smaller cone to the volume of the frustum?

A. 1 : 3
B. 1 : 7 ✓
C. 1 : 8
D. 7 : 1

Answer: B. 1 : 7
The linear scale factor of the small cone is 1/2, so its volume is 1/8 of the original cone. The frustum volume is 7/8, so the ratio is 1 : 7.

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