Chapter Exam

Chapter 12: Surface Areas and Volumes — 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 sphere of radius r is:

Answer: B. (4/3)πr³ — The standard formula for the volume of a sphere is (4/3)πr³.

Q: Fill in the blank: The total surface area of a cube of side a is ______.

Answer: C. 6a² — A cube has 6 equal square faces, each of area a², so total surface area is 6a².

Q: For a right circular cone of radius r, height h and slant height l, which relation is correct?

Answer: D. l² = r² + h² — In a right circular cone, radius, height and slant height form a right triangle, so l² = r² + h².

Q: A cylindrical tank has radius 3 m and height 7 m. Its volume is, taking π = 22/7:

Answer: A. 198 m³ — Volume of a cylinder = πr²h = (22/7) × 3² × 7 = 198 m³.

Q: A cube of side 6 cm is melted and recast into a cuboid of base 9 cm by 4 cm. The height of the cuboid is:

Answer: B. 6 cm — Volume of cube = 6³ = 216 cm³. Height of cuboid = 216/(9 × 4) = 6 cm.

Q: A solid is made by placing a hemisphere on a cylinder of the same radius. If the radius is 7 cm and the height of the cylinder is 10 cm, the total surface area of the solid is, taking π = 22/7:

Answer: A. 902 cm² — Exposed area = CSA of cylinder + CSA of hemisphere + base of cylinder = 2πrh + 2πr² + πr² = 902 cm².

Q: A toy is in the shape of a cone mounted on a hemisphere with the same radius 3 cm. If the cone has height 4 cm, the total outer surface area of the toy is:

Answer: B. 33π cm² — Slant height of cone = √(3² + 4²) = 5 cm. Total outer surface area = πrl + 2πr² = 15π + 18π = 33π cm².

Q: A metallic cone of radius 6 cm and height 8 cm is melted and recast into small spheres each of radius 1 cm. The number of spheres formed is:

Answer: B. 72 — Volume of cone = (1/3)π × 6² × 8 = 96π. Volume of one sphere = (4/3)π, so number = 96π ÷ (4π/3) = 72.

Q: A bucket is in the form of a frustum with top radius 20 cm, bottom radius 10 cm and height 24 cm. It is open at the top. If sheet metal costs Rs 2 per 100 cm², the cost of metal required is approximately, taking π = 22/7:

Answer: A. Rs 55.31 — Slant height = √(24² + 10²) = 26 cm. Area required = CSA + bottom area = π(20 + 10)26 + π(10²) = 880π cm², so cost ≈ Rs 55.31.

MATHS · CLASS 10th · Karnataka State Board

Practice Chapter 12: Surface Areas and Volumes with a free chapter-wise online MCQ test for Karnataka State Board CLASS 10th MATHS. This chapter covers: Cube Cuboid Cylinder Cone Sphere Hemisphere Frustum Surface area Curved surface area Volume Combination of solids. AI-generated questions from basic to board-exam level, with instant results and explanations.

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Chapter 12: Surface Areas and Volumes — Important Questions & Answers (FAQ)

Frequently asked questions from Karnataka State Board CLASS 10th MATHS — Chapter 12: Surface Areas and Volumes, 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 sphere of radius r is:

A. 4πr²
B. (4/3)πr³ ✓
C. (2/3)πr³
D. πr²h

Answer: B. (4/3)πr³
The standard formula for the volume of a sphere is (4/3)πr³.

Fill in the blank: The total surface area of a cube of side a is ______.

A. a³
B. 4a²
C. 6a² ✓
D. 12a²

Answer: C. 6a²
A cube has 6 equal square faces, each of area a², so total surface area is 6a².

For a right circular cone of radius r, height h and slant height l, which relation is correct?

A. l = r + h
B. l² = r² - h²
C. h² = l² + r²
D. l² = r² + h² ✓

Answer: D. l² = r² + h²
In a right circular cone, radius, height and slant height form a right triangle, so l² = r² + h².

A cylindrical tank has radius 3 m and height 7 m. Its volume is, taking π = 22/7:

A. 198 m³ ✓
B. 154 m³
C. 132 m³
D. 231 m³

Answer: A. 198 m³
Volume of a cylinder = πr²h = (22/7) × 3² × 7 = 198 m³.

A cube of side 6 cm is melted and recast into a cuboid of base 9 cm by 4 cm. The height of the cuboid is:

A. 4 cm
B. 6 cm ✓
C. 8 cm
D. 12 cm

Answer: B. 6 cm
Volume of cube = 6³ = 216 cm³. Height of cuboid = 216/(9 × 4) = 6 cm.

A solid is made by placing a hemisphere on a cylinder of the same radius. If the radius is 7 cm and the height of the cylinder is 10 cm, the total surface area of the solid is, taking π = 22/7:

A. 902 cm² ✓
B. 748 cm²
C. 1056 cm²
D. 594 cm²

Answer: A. 902 cm²
Exposed area = CSA of cylinder + CSA of hemisphere + base of cylinder = 2πrh + 2πr² + πr² = 902 cm².

A toy is in the shape of a cone mounted on a hemisphere with the same radius 3 cm. If the cone has height 4 cm, the total outer surface area of the toy is:

A. 24π cm²
B. 33π cm² ✓
C. 42π cm²
D. 48π cm²

Answer: B. 33π cm²
Slant height of cone = √(3² + 4²) = 5 cm. Total outer surface area = πrl + 2πr² = 15π + 18π = 33π cm².

A metallic cone of radius 6 cm and height 8 cm is melted and recast into small spheres each of radius 1 cm. The number of spheres formed is:

A. 64
B. 72 ✓
C. 84
D. 96

Answer: B. 72
Volume of cone = (1/3)π × 6² × 8 = 96π. Volume of one sphere = (4/3)π, so number = 96π ÷ (4π/3) = 72.

A bucket is in the form of a frustum with top radius 20 cm, bottom radius 10 cm and height 24 cm. It is open at the top. If sheet metal costs Rs 2 per 100 cm², the cost of metal required is approximately, taking π = 22/7:

A. Rs 55.31 ✓
B. Rs 49.03
C. Rs 62.86
D. Rs 44.00

Answer: A. Rs 55.31
Slant height = √(24² + 10²) = 26 cm. Area required = CSA + bottom area = π(20 + 10)26 + π(10²) = 880π cm², so cost ≈ Rs 55.31.

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