There are 33 MCQ questions for Chapter 11, “Surface Areas and Volumes”. Go slow while solving these questions. The solution is hidden by purpose. Give your best shot and then check the answer.
Class 9th Maths Important MCQs with Answers from Chapter 11 – Surface Areas and Volumes
Question 1. What is the curved surface area of a right circular cone with radius 7 cm and slant height 10 cm?
a) 220 cm²
b) 150 cm²
c) 110 cm²
d) 250 cm²
Answer:
a) 220 cm² — The formula for curved surface area of a cone is πrl. Substituting π = 22/7, r = 7, and l = 10: π × 7 × 10 = 220 cm².
Question 2. If the radius of a sphere is 14 cm, what is its surface area?
a) 2464 cm²
b) 2462 cm²
c) 2400 cm²
d) 2412 cm²
Answer:
a) 2464 cm² — The surface area of a sphere is 4πr². Substituting π = 22/7 and r = 14: 4 × π × 14² = 2464 cm².
Question 3. What is the volume of a cone with radius 3.5 cm and height 12 cm?
a) 154 cm³
b) 154.5 cm³
c) 150 cm³
d) 153 cm³
Answer:
a) 154 cm³ — The volume of a cone is (1/3)πr²h. Substituting π = 22/7, r = 3.5, and h = 12: (1/3) × π × 3.5² × 12 = 154 cm³.
Question 4. The diameter of a hemisphere is 10 cm. What is its total surface area?
a) 250 cm²
b) 250.57 cm²
c) 260 cm²
d) 259.28 cm²
Answer:
d) 259.28 cm² — Total surface area of a hemisphere is 3πr². Radius = 10/2 = 5 cm. 3 × π × 5² = 259.28 cm².
Question 5. If the slant height of a cone is 21 cm and its radius is 7 cm, what is the total surface area?
a) 462 cm²
b) 518 cm²
c) 514 cm²
d) 520 cm²
Answer:
b) 518 cm² — Total surface area of a cone is πr(l + r). Substituting π = 22/7, r = 7, and l = 21: π × 7 × (21 + 7) = 518 cm².
Question 6. A sphere has a surface area of 154 cm². What is its radius?
a) 3.5 cm
b) 4.5 cm
c) 4 cm
d) 5 cm
Answer:
a) 3.5 cm — Surface area of a sphere is 4πr². Substituting π = 22/7 and solving for r, we get r = 3.5 cm.
Question 7. If the base radius of a cone is 6 cm and its height is 8 cm, what is the slant height?
a) 8 cm
b) 10 cm
c) 12 cm
d) 14 cm
Answer:
b) 10 cm — The slant height is given by l = √(r² + h²). Substituting r = 6 and h = 8: l = √(6² + 8²) = 10 cm.
Question 8. What is the curved surface area of a hemisphere with a radius of 7 cm?
a) 308 cm²
b) 314 cm²
c) 310 cm²
d) 300 cm²
Answer:
a) 308 cm² — Curved surface area of a hemisphere is 2πr². Substituting π = 22/7 and r = 7: 2 × π × 7² = 308 cm².
Question 9. The diameter of a sphere is 14 cm. What is its volume?
a) 1436 cm³
b) 1436.76 cm³
c) 1435 cm³
d) 1430 cm³
Answer:
b) 1436.76 cm³ — Volume of a sphere is (4/3)πr³. Radius = 14/2 = 7 cm. Substituting π = 22/7: (4/3) × π × 7³ = 1436.76 cm³.
Question 10. A cone has a base radius of 7 cm and slant height of 25 cm. What is its curved surface area?
a) 550 cm²
b) 555 cm²
c) 560 cm²
d) 565 cm²
Answer:
c) 560 cm² — Curved surface area of a cone is πrl. Substituting π = 22/7, r = 7, and l = 25: π × 7 × 25 = 560 cm².
Question 11. A cone has a base diameter of 12 cm and height of 9 cm. What is its slant height?
a) 15 cm
b) 12 cm
c) 10 cm
d) 13 cm
Answer:
d) 13 cm — The slant height is given by √(r² + h²). Radius = 12/2 = 6 cm, height = 9 cm: √(6² + 9²) = 13 cm.
Question 12. What is the total surface area of a hemisphere with a radius of 3.5 cm?
a) 77 cm²
b) 77.5 cm²
c) 79 cm²
d) 82 cm²
Answer:
a) 77 cm² — Total surface area of a hemisphere is 3πr². Substituting π = 22/7, r = 3.5: 3 × π × (3.5)² = 77 cm².
Question 13. A sphere has a radius of 10 cm. What is its volume?
a) 4188.67 cm³
b) 4200 cm³
c) 4150 cm³
d) 4190 cm³
Answer:
a) 4188.67 cm³ — Volume of a sphere is (4/3)πr³. Substituting π = 3.14 and r = 10: (4/3) × 3.14 × 10³ = 4188.67 cm³.
Question 14. A cone has a height of 12 cm and slant height of 13 cm. What is its base radius?
a) 6 cm
b) 7 cm
c) 5 cm
d) 8 cm
Answer:
c) 5 cm — Using l² = r² + h², substitute l = 13 and h = 12: r² = 13² – 12² = 25, so r = 5 cm.
Question 15. The curved surface area of a cone is 231 cm² and its base radius is 7 cm. What is the slant height?
a) 10 cm
b) 9 cm
c) 11 cm
d) 12 cm
Answer:
c) 11 cm — Curved surface area is πrl. Substituting π = 22/7, r = 7: 231 = π × 7 × l, so l = 11 cm.
Question 16. A hemispherical dome has a base radius of 10.5 m. What is its curved surface area?
a) 693 m²
b) 694 m²
c) 690 m²
d) 700 m²
Answer:
a) 693 m² — Curved surface area of a hemisphere is 2πr². Substituting π = 22/7, r = 10.5: 2 × π × (10.5)² = 693 m².
Question 17. If a sphere and a cylinder have the same radius r and height 2r, what is the ratio of their volumes?
a) 2:3
b) 3:2
c) 3:1
d) 1:2
Answer:
c) 3:1 — Volume of a sphere is (4/3)πr³, and volume of the cylinder is πr² × 2r. Ratio = (4/3)πr³ : πr³ × 2 = 3:1.
Question 18. A cone has a volume of 154 cm³ and a base radius of 7 cm. What is its height?
a) 6 cm
b) 8 cm
c) 10 cm
d) 12 cm
Answer:
a) 6 cm — Volume of a cone is (1/3)πr²h. Substituting π = 22/7, r = 7: 154 = (1/3) × π × 7² × h, so h = 6 cm.
Question 19. The diameter of a metallic sphere is 10 cm. What is its surface area?
a) 314 cm²
b) 312 cm²
c) 320 cm²
d) 315 cm²
Answer:
a) 314 cm² — Surface area of a sphere is 4πr². Radius = 10/2 = 5 cm. Substituting π = 3.14: 4 × π × (5)² = 314 cm².
Question 20. A cone has a base radius of 6 cm and a slant height of 10 cm. What is its total surface area?
a) 285 cm²
b) 290 cm²
c) 295 cm²
d) 300 cm²
Answer:
a) 285 cm² — Total surface area of a cone is πr(l + r). Substituting π = 3.14, r = 6, l = 10: π × 6 × (10 + 6) = 285 cm².
Question 21. What is the volume of a hemisphere with a radius of 7 cm?
a) 718.67 cm³
b) 716.67 cm³
c) 720 cm³
d) 715 cm³
Answer:
a) 718.67 cm³ — Volume of a hemisphere is (2/3)πr³. Substituting π = 22/7 and r = 7: (2/3) × π × (7)³ = 718.67 cm³.
Question 22. A cone has a slant height of 17 cm and base radius of 8 cm. What is its curved surface area?
a) 428 cm²
b) 429 cm²
c) 430 cm²
d) 432 cm²
Answer:
a) 428 cm² — Curved surface area of a cone is πrl. Substituting π = 22/7, r = 8, l = 17: π × 8 × 17 = 428 cm².
Question 23. A sphere has a surface area of 113.04 cm². What is its radius?
a) 3 cm
b) 3.5 cm
c) 4 cm
d) 2.5 cm
Answer:
b) 3.5 cm — Surface area of a sphere is 4πr². Substituting π = 3.14 and solving for r, we get r = 3.5 cm.
Question 24. The diameter of a cone’s base is 12 cm and its height is 16 cm. What is its volume?
a) 603 cm³
b) 604.8 cm³
c) 606 cm³
d) 608 cm³
Answer:
b) 604.8 cm³ — Volume of a cone is (1/3)πr²h. Radius = 12/2 = 6 cm. Substituting π = 3.14 and h = 16: (1/3) × π × 6² × 16 = 604.8 cm³.
Question 25. A hemisphere has a surface area of 346.36 cm². What is its radius?
a) 6 cm
b) 5 cm
c) 7 cm
d) 5.5 cm
Answer:
b) 5 cm — Surface area of a hemisphere is 3πr². Substituting π = 3.14 and solving for r, we get r = 5 cm.
Question 26. A cone has a slant height of 13 cm and a curved surface area of 143 cm². What is its base radius?
a) 7 cm
b) 6 cm
c) 5.5 cm
d) 5 cm
Answer:
d) 5 cm — Curved surface area is πrl. Substituting π = 22/7, l = 13: 143 = π × r × 13, so r = 5 cm.
Question 27. A sphere has a diameter of 14 cm. What is its total surface area?
a) 616 cm²
b) 615 cm²
c) 620 cm²
d) 612 cm²
Answer:
a) 616 cm² — Surface area of a sphere is 4πr². Radius = 14/2 = 7 cm. Substituting π = 22/7: 4 × π × 7² = 616 cm².
Question 28. What is the total surface area of a cone with base radius 3 cm and slant height 5 cm?
a) 75.42 cm²
b) 75.40 cm²
c) 75 cm²
d) 74.5 cm²
Answer:
a) 75.42 cm² — Total surface area of a cone is πr(l + r). Substituting π = 3.14, r = 3, l = 5: π × 3 × (5 + 3) = 75.42 cm².
Question 29. A hemisphere has a curved surface area of 154 cm². What is its radius?
a) 7 cm
b) 6 cm
c) 5.5 cm
d) 5 cm
Answer:
a) 7 cm — Curved surface area of a hemisphere is 2πr². Substituting π = 22/7 and solving for r, we get r = 7 cm.
Question 30. A cone and a cylinder have the same base radius and height. What is the ratio of their volumes?
a) 1:1
b) 1:2
c) 1:3
d) 1:4
Answer:
c) 1:3 — The volume of a cone is (1/3)πr²h, while the volume of a cylinder is πr²h. Ratio = (1/3)πr²h : πr²h = 1:3.
Question 31. A cone has a base radius of 4 cm and height of 9 cm. What is its slant height?
a) 10 cm
b) 11 cm
c) 12 cm
d) 13 cm
Answer:
b) 11 cm — Slant height is given by √(r² + h²). Substituting r = 4 and h = 9: √(4² + 9²) = √(16 + 81) = √97 ≈ 11 cm.
Question 32. A metallic sphere is melted to form 8 smaller spheres of equal size. If the radius of the original sphere is 6 cm, what is the radius of each smaller sphere?
a) 3 cm
b) 2 cm
c) 4 cm
d) 2.5 cm
Answer:
a) 3 cm — Volume is conserved. Volume of original sphere = (4/3)πR³. Volume of each smaller sphere = (4/3)πr³. Solving R³ = 8r³: 6³ = 8r³, so r = 3 cm.
Question 33. A cone has a volume of 200 cm³ and a base radius of 5 cm. What is its height?
a) 6 cm
b) 7 cm
c) 8 cm
d) 9 cm
Answer:
a) 6 cm — Volume of a cone is (1/3)πr²h. Substituting π = 3.14, r = 5: 200 = (1/3)π(5)²h, so h = 6 cm.
