Chapter 12: Surface Areas and Volumes — Online MCQ Test
MATHS · Grade 10 · CBSE(NCERT)
Practice Chapter 12: Surface Areas and Volumes with a free chapter-wise online MCQ test.
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.
Chapter 12: Surface Areas and Volumes — Important Questions & Answers
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 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.
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.
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.
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.
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.
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.
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.
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.
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.
Slant height = √(24² + 10²) = 26 cm. Area required = CSA + bottom area = π(20 + 10)26 + π(10²) = 880π cm², so cost ≈ Rs 55.31.