MATHEMATICS CLASS- 10
MCQ- CH-12(Surface areas and volumes)
Class 10 Mathematics
Chapter 12: Surface Areas and Volumes
50 Board-Level MCQs with Answers and Solutions
Q1. The curved surface area of a cylinder is
(a) πr²h
(b) 2πrh
(c) 2πr(r+h)
(d) πrh
Answer: (b) 2πrh
Q2. The volume of a cylinder is
(a) πr²h
(b) 2πrh
(c) πrh
(d) 2πr²h
Answer: (a) πr²h
Q3. Total surface area of a cylinder is
(a) 2πrh
(b) πr²h
(c) 2πr(r+h)
(d) πr(r+h)
Answer: (c)
Q4. Volume of a cone is
(a) πr²h
(b) 1/2 πr²h
(c) 1/3 πr²h
(d) 2/3 πr²h
Answer: (c)
Q5. Curved surface area of a cone is
(a) πrl
(b) πr²
(c) 2πrh
(d) πr²h
Answer: (a)
Q6. The volume of a sphere is
(a) 4πr²
(b) 4/3 πr³
(c) 2/3 πr³
(d) πr³
Answer: (b)
Q7. Surface area of a sphere is
(a) 2πr²
(b) 3πr²
(c) 4πr²
(d) πr²
Answer: (c)
Q8. The slant height of a cone is given by
(a) √(r²+h²)
(b) r+h
(c) r²+h²
(d) h-r
Answer: (a)
Q9. A hemisphere is
(a) Half of a cone
(b) Half of a cylinder
(c) Half of a sphere
(d) Quarter of a sphere
Answer: (c)
Q10. Volume of a hemisphere is
(a) 2/3 πr³
(b) 4/3 πr³
(c) πr³
(d) 1/3 πr³
Answer: (a)
Q11. The total surface area of a sphere of radius 7 cm is
(a) 616 cm²
(b) 308 cm²
(c) 154 cm²
(d) 770 cm²
Answer: (a)
Solution: 4πr² = 4 × 22/7 × 7 × 7 = 616 cm².
Q12. Volume of a cube of side 5 cm is
(a) 25 cm³
(b) 100 cm³
(c) 125 cm³
(d) 150 cm³
Answer: (c)
Q13. Total surface area of a cube is
(a) 4a²
(b) 5a²
(c) 6a²
(d) a³
Answer: (c)
Q14. Volume of a cuboid is
(a) l+b+h
(b) lbh
(c) 2(l+b+h)
(d) lb+h
Answer: (b)
Q15. Total surface area of a cuboid is
(a) 2(lb+bh+hl)
(b) lbh
(c) lb+bh+hl
(d) 2lbh
Answer: (a)
Q16. A cone and cylinder have same base radius and height. The volume of cone is
(a) Equal to cylinder
(b) Half of cylinder
(c) One-third of cylinder
(d) Double of cylinder
Answer: (c)
Q17. Curved surface area of a hemisphere is
(a) 2πr²
(b) 3πr²
(c) 4πr²
(d) πr²
Answer: (a)
Q18. Total surface area of a hemisphere is
(a) 2πr²
(b) 3πr²
(c) 4πr²
(d) πr²
Answer: (b)
Q19. If radius of a sphere doubles, its volume becomes
(a) 2 times
(b) 4 times
(c) 6 times
(d) 8 times
Answer: (d)
Q20. If radius of a sphere doubles, surface area becomes
(a) 2 times
(b) 4 times
(c) 6 times
(d) 8 times
Answer: (b)
Q21. (CBSE PYQ) Volume of a cylinder of radius 7 cm and height 10 cm is
(a) 1540 cm³
(b) 1440 cm³
(c) 1640 cm³
(d) 1500 cm³
Answer: (a)
Q22. The units of volume are
(a) cm
(b) cm²
(c) cm³
(d) m
Answer: (c)
Q23. The units of surface area are
(a) cm
(b) cm²
(c) cm³
(d) litre
Answer: (b)
Q24. Volume of a sphere of radius 3 cm is
(a) 36π cm³
(b) 27π cm³
(c) 18π cm³
(d) 12π cm³
Answer: (a)
Q25. The slant height of a cone with r = 5 cm and h = 12 cm is
(a) 10 cm
(b) 12 cm
(c) 13 cm
(d) 15 cm
Answer: (c)
Solution: l = √(5²+12²)=13 cm.
Q26. (CBSE PYQ) Curved surface area of a cylinder of radius 7 cm and height 10 cm is
(a) 440 cm²
(b) 220 cm²
(c) 154 cm²
(d) 308 cm²
Answer: (a)
Q27. Volume of a cone of radius 3 cm and height 7 cm is
(a) 21π cm³
(b) 42π cm³
(c) 63π cm³
(d) 84π cm³
Answer: (a)
Q28. Total surface area of a cone is
(a) πrl
(b) πr(l+r)
(c) πr²
(d) 2πrh
Answer: (b)
Q29. Volume of a hemisphere is exactly
(a) Half volume of sphere
(b) Double volume of sphere
(c) One-third volume of sphere
(d) One-fourth volume of sphere
Answer: (a)
Q30. A sphere of radius 14 cm has diameter
(a) 14 cm
(b) 21 cm
(c) 28 cm
(d) 42 cm
Answer: (c)
Q31. If side of a cube is doubled, volume becomes
(a) 2 times
(b) 4 times
(c) 6 times
(d) 8 times
Answer: (d)
Q32. If side of a cube doubles, surface area becomes
(a) 2 times
(b) 4 times
(c) 6 times
(d) 8 times
Answer: (b)
Q33. The volume of a cuboid 4 cm × 5 cm × 6 cm is
(a) 100 cm³
(b) 110 cm³
(c) 120 cm³
(d) 130 cm³
Answer: (c)
Q34. Total surface area of a cube of side 4 cm is
(a) 64 cm²
(b) 96 cm²
(c) 128 cm²
(d) 256 cm²
Answer: (b)
Q35. Which solid has no vertex?
(a) Cone
(b) Cube
(c) Sphere
(d) Cuboid
Answer: (c)
Q36. (CBSE PYQ) Total surface area of a sphere of radius 14 cm is
(a) 2464 cm²
(b) 1232 cm²
(c) 616 cm²
(d) 308 cm²
Answer: (a)
Q37. Which solid has one curved surface and one circular base?
(a) Cylinder
(b) Sphere
(c) Cone
(d) Cube
Answer: (c)
Q38. A cylinder has
(a) One circular base
(b) Two circular bases
(c) No base
(d) Three bases
Answer: (b)
Q39. A sphere has
(a) One face
(b) One curved surface only
(c) Two faces
(d) One edge
Answer: (b)
Q40. Volume of a sphere of radius 7 cm is
(a) 1437.33 cm³
(b) 1337.33 cm³
(c) 1237.33 cm³
(d) 1537.33 cm³
Answer: (a)
Q41. If radius and height of a cylinder are doubled, volume becomes
(a) 4 times
(b) 6 times
(c) 8 times
(d) 12 times
Answer: (c)
Q42. Curved surface area of a cylinder of radius 3 cm and height 7 cm is
(a) 132 cm²
(b) 66π cm²
(c) 42π cm²
(d) 21π cm²
Answer: (c)
Q43. Which formula gives volume of a sphere?
(a) 4πr²
(b) πr²h
(c) 4/3 πr³
(d) 2πrh
Answer: (c)
Q44. Which formula gives curved surface area of a cone?
(a) πrl
(b) πr²
(c) 2πrh
(d) πr²h
Answer: (a)
Q45. If radius of a cone is 7 cm and slant height is 10 cm, CSA is
(a) 220 cm²
(b) 154 cm²
(c) 440 cm²
(d) 110 cm²
Answer: (a)
Q46. The capacity of a container is measured by its
(a) Area
(b) Perimeter
(c) Volume
(d) Radius
Answer: (c)
Q47. One litre equals
(a) 100 cm³
(b) 1000 cm³
(c) 10000 cm³
(d) 10 cm³
Answer: (b)
Q48. Which solid has exactly one vertex?
(a) Sphere
(b) Cylinder
(c) Cone
(d) Cuboid
Answer: (c)
Q49. Volume of a cube of side 10 cm is
(a) 100 cm³
(b) 500 cm³
(c) 1000 cm³
(d) 1200 cm³
Answer: (c)
Q50. Which statement is true?
(a) Volume is measured in square units.
(b) Surface area is measured in cubic units.
(c) Volume measures space occupied by a solid.
(d) Sphere has edges and vertices.
Answer: (c) Volume measures space occupied by a solid.
Solution: Volume represents the three-dimensional space occupied by a solid and is measured in cubic units.