The Surface Areas and Volumes chapter of Class 10 Maths helps students understand how to calculate the surface areas and volumes of three-dimensional shapes. It covers important concepts related to cones, cylinders, spheres, hemispheres, and frustums, along with their surface areas and volume calculations.
The chapter focuses on applying formulas and solving practical measurement problems involving solid shapes. Regular practice helps students improve their mensuration skills, calculation accuracy, and problem-solving abilities for CBSE board exams. Practicing chapter-wise MCQs and preparing through CBSE Board resources and MCQs Class 10 Maths can help students revise important concepts and prepare according to the latest syllabus.
Topics Covered
Before solving Surface Areas and Volumes Class 10 MCQs with Answers, students should revise all important formulas and concepts carefully because most objective questions are directly formula and figure based. Important concepts covered in this chapter :
- Cone
- Cylinder
- Sphere
- Hemisphere
- Frustum of cone
- Curved surface area
- Total surface area
- Volume calculations
- Radius and diameter relationships
- Height and slant height
- Capacity measurements
- Solid figure combinations
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MCQs for Class 10 Maths Chapter 12 Surface Areas and Volumes with Answers and Explanations
Revise the Statistics chapter with these Class 10 Maths objective questions. These objective questions help students strengthen formula understanding, mensuration calculations, 3D figure analysis, and board exam preparation skills.
Q1. A cone has radius 6 cm and height 8 cm. Find its slant height.
- A) 8 cm
B) 9 cm
C) 10 cm
D) 12 cm
Answer: C
Explanation:
Slant height = sqrt(r^2 + h^2)
= sqrt(6^2 + 8^2)
= sqrt(36 + 64)
= sqrt(100) = 10 cm.
Q2. Find the curved surface area of a cylinder having radius 7 cm and height 15 cm.
- A) 550 sq cm
B) 660 sq cm
C) 770 sq cm
D) 880 sq cm
Answer: B
Explanation:
Curved surface area = 2pi rh
= 2 x (22/7) x 7 x 15
= 660 sq cm.
Q3. The volume of a cube with side 11 cm is:
- A) 121 cubic cm
B) 726 cubic cm
C) 1331 cubic cm
D) 1452 cubic cm
Answer: C
Explanation:
Volume of cube = side^3
= 11^3 = 1331 cubic cm.
Q4. A sphere has radius 14 cm. Find its volume.
- A) 11494.67 cubic cm
B) 11500 cubic cm
C) 12000 cubic cm
D) 11088 cubic cm
Answer: A
Explanation:
Volume of sphere = (4/3)pi r^3
= (4/3) x (22/7) x 14 x 14 x 14
≈ 11494.67 cubic cm.
Q5. Find the total surface area of a hemisphere of radius 7 cm.
- A) 308 sq cm
B) 462 sq cm
C) 616 sq cm
D) 154 sq cm
Answer: B
Explanation:
Total surface area of hemisphere = 3pi r^2
= 3 x (22/7) x 7 x 7
= 462 sq cm.
Q6. The curved surface area of a cone with radius 5 cm and slant height 12 cm is:
- A) 60pi sq cm
B) 50pi sq cm
C) 70pi sq cm
D) 80pi sq cm
Answer: A
Explanation:
CSA of cone = pi r l
= pi x 5 x 12
= 60pi sq cm.
Q7. A cuboid has dimensions 15 cm x 8 cm x 6 cm. Find its volume.
- A) 620 cubic cm
B) 720 cubic cm
C) 840 cubic cm
D) 900 cubic cm
Answer: B
Explanation:
Volume = l x b x h
= 15 x 8 x 6
= 720 cubic cm.
Q8. The radius of a sphere is doubled. Its surface area becomes:
- A) 2 times
B) 3 times
C) 4 times
D) 8 times
Answer: C
Explanation:
Surface area depends on r^2.
If the radius doubles, the area becomes 2^2 = 4 times.
Q9. Find the volume of a cylinder with radius 4 cm and height 21 cm.
- A) 336pi cubic cm
B) 420pi cubic cm
C) 252pi cubic cm
D) 168pi cubic cm
Answer: A
Explanation:
Volume = pi r^2 h
= pi x 4^2 x 21
= 336pi cubic cm.
Q10. A cone has height 24 cm and radius 7 cm. Find its slant height.
- A) 24 cm
B) 25 cm
C) 26 cm
D) 27 cm
Answer: B
Explanation:
l = sqrt(h^2 + r^2)
= sqrt(24^2 + 7^2)
= sqrt(576 + 49)
= sqrt(625) = 25 cm.
Q11. The total surface area of a cube with side 9 cm is:
- A) 324 sq cm
B) 486 sq cm
C) 576 sq cm
D) 729 sq cm
Answer: B
Explanation:
TSA of cube = 6a^2
= 6 x 9^2
= 6 x 81
= 486 sq cm.
Q12. Find the curved surface area of a hemisphere of radius 14 cm.
- A) 1232 sq cm
B) 616 sq cm
C) 2464 sq cm
D) 1848 sq cm
Answer: A
Explanation:
CSA of hemisphere = 2pi r^2
= 2 x (22/7) x 14 x 14
= 1232 sq cm.
Q13. A cone and cylinder have the same base radius and height. Find the ratio of their volumes.
- A) 1:2
B) 1:3
C) 2:3
D) 3:1
Answer: B
Explanation:
Volume of cone = (1/3)pi r^2 h
Volume of cylinder = pi r^2 h
Ratio = 1:3.
Q14. Find the total surface area of a cylinder with radius 3.5 cm and height 10 cm.
- A) 231 sq cm
B) 275 sq cm
C) 300 sq cm
D) 350 sq cm
Answer: A
Explanation:
TSA = 2pi r(r + h)
= 2 x (22/7) x 3.5 x (3.5 + 10)
= 231 sq cm.
Q15. The volume of a hemisphere of radius 6 cm is:
- A) 144pi cubic cm
B) 288pi cubic cm
C) 72pi cubic cm
D) 216pi cubic cm
Answer: A
Explanation:
Volume of hemisphere = (2/3)pi r^3
= (2/3)pi x 6^3
= 144pi cubic cm.
Q16. A sphere has diameter 18 cm. Find its surface area.
- A) 972pi sq cm
B) 648pi sq cm
C) 324pi sq cm
D) 486pi sq cm
Answer: C
Explanation:
Radius = 18/2 = 9 cm
Surface area = 4pi r^2
= 4pi x 9^2
= 324pi sq cm.
Q17. Find the height of a cone whose slant height is 13 cm and radius is 5 cm.
- A) 10 cm
B) 11 cm
C) 12 cm
D) 14 cm
Answer: C
Explanation:
h = sqrt(l^2 - r^2)
= sqrt(13^2 - 5^2)
= sqrt(169 - 25)
= sqrt(144) = 12 cm.
Q18. The radius of a cylinder is 7 cm and height is 20 cm. Find its volume.
- A) 3080 cubic cm
B) 2800 cubic cm
C) 3200 cubic cm
D) 2500 cubic cm
Answer: A
Explanation:
Volume = pi r^2 h
= (22/7) x 7 x 7 x 20
= 3080 cubic cm.
Q19. Find the volume of a cone with radius 6 cm and height 14 cm.
- A) 168pi cubic cm
B) 196pi cubic cm
C) 210pi cubic cm
D) 252pi cubic cm
Answer: A
Explanation:
Volume = (1/3)pi r^2 h
= (1/3)pi x 6^2 x 14
= 168pi cubic cm.
Q20. The total surface area of a sphere of radius 7 cm is:
- A) 616 sq cm
B) 462 sq cm
C) 308 sq cm
D) 154 sq cm
Answer: A
Explanation:
Surface area = 4pi r^2
= 4 x (22/7) x 7 x 7
= 616 sq cm.
Q21. A metallic cube of side 6 cm is melted to form small cubes of side 2 cm. Find the number of small cubes formed.
- A) 9
B) 18
C) 27
D) 36
Answer: C
Explanation:
Number of cubes = (6^3)/(2^3)
= 216/8
= 27.
Q22. Find the curved surface area of a cone with radius 14 cm and slant height 20 cm.
- A) 280pi sq cm
B) 300pi sq cm
C) 240pi sq cm
D) 350pi sq cm
Answer: A
Explanation:
CSA = pi r l
= pi x 14 x 20
= 280pi sq cm.
Q23. A cuboid has dimensions 18 cm x 10 cm x 5 cm. Find its total surface area.
- A) 640 sq cm
B) 720 sq cm
C) 560 sq cm
D) 460 sq cm
Answer: C
Explanation:
TSA = 2(lb + bh + hl)
= 2(18x10 + 10x5 + 18x5)
= 2(180 + 50 + 90)
= 640 sq cm.
Q24. Find the radius of a sphere whose volume is 288pi cubic cm.
- A) 4 cm
B) 5 cm
C) 6 cm
D) 7 cm
Answer: C
Explanation:
(4/3)pi r^3 = 288pi
r^3 = 216
r = 6 cm.
Q25. The slant height of a cone is 15 cm and radius is 9 cm. Find its height.
- A) 10 cm
B) 11 cm
C) 12 cm
D) 13 cm
Answer: C
Explanation:
Height = sqrt(15^2 - 9^2)
= sqrt(225 - 81)
= sqrt(144) = 12 cm.
Q26. A cylinder has radius 5 cm and height 18 cm. Find its curved surface area.
- A) 540pi sq cm
B) 180pi sq cm
C) 90pi sq cm
D) 360pi sq cm
Answer: B
Explanation:
CSA = 2pi rh
= 2pi x 5 x 18
= 180pi sq cm.
Q27. A sphere of radius 12 cm is melted into spheres of radius 3 cm. Find the number of small spheres formed.
- A) 16
B) 32
C) 64
D) 128
Answer: C
Explanation:
Number of spheres = (12^3)/(3^3)
= 1728/27
= 64.
Q28. Find the total surface area of a cone with radius 7 cm and slant height 24 cm.
- A) 217pi sq cm
B) 224pi sq cm
C) 231pi sq cm
D) 248pi sq cm
Answer: A
Explanation:
TSA = pi r(r + l)
= pi x 7 x (7 + 24)
= 217pi sq cm.
Q29. The volume of a sphere is 1372/3 pi cubic cm. Find its radius.
- A) 5 cm
B) 6 cm
C) 7 cm
D) 8 cm
Answer: C
Explanation:
(4/3)pi r^3 = (1372/3)pi
4r^3 = 1372
r^3 = 343
r = 7 cm.
Q30. Find the total surface area of a cuboid having dimensions 12 cm x 9 cm x 5 cm.
- A) 426 sq cm
B) 438 sq cm
C) 456 sq cm
D) 468 sq cm
Answer: A
Explanation:
TSA = 2(lb + bh + hl)
= 2(12x9 + 9x5 + 12x5)
= 2(108 + 45 + 60)
= 426 sq cm.
Class 10 Chapter 12 Important Formulas
The following formulas are extremely important for solving Surface Areas and Volumes MCQs Class 10 and board exam questions.
| Shape | Formula |
| Volume of Cylinder | πr²h |
| Curved Surface Area of Cylinder | 2πrh |
| Total Surface Area of Cylinder | 2πr(r + h) |
| Volume of Cone | (1/3)πr²h |
| Curved Surface Area of Cone | πrl |
| Total Surface Area of Cone | πr(l + r) |
| Volume of Sphere | (4/3)πr³ |
| Surface Area of Sphere | 4πr² |
| Volume of Hemisphere | (2/3)πr³ |
| Total Surface Area of Hemisphere | 3πr² |
Students should revise these formulas regularly because many Surface Areas and Volumes Class 10 objective questions are directly calculation based.
Class 10 Chapter 12 Important Terms
The following terms are very important for solving Surface Areas and Volumes Class 10 MCQs with Answers correctly.
| Term | Meaning |
| Radius | Distance from center to boundary |
| Diameter | Double of radius |
| Height | Vertical measurement of solid |
| Slant Height | Inclined height of cone |
| Curved Surface Area (CSA) | Outer curved covering only |
| Total Surface Area (TSA) | Complete outer surface |
| Volume | Total space occupied by solid |
