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NCERT Class 10 Maths Chapter 12 Online Test – Surface Areas and Volumes (50 MCQs) | Board Exam 2026

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NCERT Class 10 Maths Chapter 12 Online Test – Surface Areas and Volumes (50 MCQs)
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NCERT Class 10 Maths – Chapter 12: Surface Areas and Volumes

Board Exam 2026 Online Test (Strictly NCERT Based)

Q1. The curved surface area of a sphere of radius r is:

4πr2
πr2
2πr2
πr
CSA of a sphere = 4πr2.

Q2. The volume of a sphere of radius r is:

πr3
(4/3)πr3
2πr3
(1/3)πr3
Volume of sphere = (4/3)πr3.

Q3. The curved surface area of a cylinder is:

πr2
2πr2
2πrh
πrh
CSA of cylinder = 2πrh.

Q4. The total surface area of a cube of side a is:

6a2
a2
12a2
3a2
A cube has 6 square faces each of area a2.

Q5. The volume of a cone is:

πr2h
2πr2h
(2/3)πr2h
(1/3)πr2h
Volume of cone = (1/3)πr2h.

Q6. The slant height of a cone is:

r + h
√(r2 + h2)
r − h
2r
Slant height l = √(r2 + h2).

Q7. The curved surface area of a cone is:

πr2
2πrh
πrl
πr
CSA of cone = πrl.

Q8. The total surface area of a sphere is:

4πr2
2πr2
πr2
πr
TSA of sphere = 4πr2.

Q9. The volume of a cylinder is:

2πrh
πr2h
πr2
πrh
Volume of cylinder = πr2h.

Q10. The unit of volume is:

cm
cm2
m
cm3
Volume is measured in cubic units.

Q11. A solid made by rotating a rectangle about one side is:

Cylinder
Cone
Sphere
Cube
Rotation of rectangle forms a cylinder.

Q12. A solid made by rotating a triangle about one side is:

Cylinder
Cone
Sphere
Cube
Rotation of a right triangle forms a cone.

Q13. The total surface area of a cylinder is:

2πrh
πr2h
2πr(h + r)
πr(h + r)
TSA of cylinder = 2πr(h + r).

Q14. The curved surface area of a hemisphere is:

πr2
2πr2
3πr2
2πr2
CSA of hemisphere = 2πr2.

Q15. The volume of a hemisphere is:

(4/3)πr3
(2/3)πr3
(1/3)πr3
πr3
Volume of hemisphere = (2/3)πr3.

Q16. The total surface area of a hemisphere is:

3πr2
2πr2
4πr2
πr2
TSA of hemisphere = 3πr2.

Q17. Which solid has only curved surface?

Cone
Cylinder
Sphere
Cube
A sphere has no flat surface.

Q18. The base of a cone is:

Square
Circle
Triangle
Rectangle
Base of cone is circular.

Q19. The height of a cylinder is the distance between:

Two radii
Two diameters
Centre and surface
Two circular bases
Height is distance between the two circular bases.

Q20. If radius of a sphere is doubled, its volume becomes:

Eight times
Four times
Double
Same
Volume ∝ r3.

Q21. If height of a cylinder is doubled, volume becomes:

Four times
Double
Half
Same
Volume is directly proportional to height.

Q22. The curved surface area of a hemisphere is half of:

Cube
Cone
Sphere
Cylinder
CSA of hemisphere is half of sphere.

Q23. The shape having maximum volume for given surface area is:

Cube
Cone
Cylinder
Sphere
Sphere encloses maximum volume.

Q24. A solid formed by rotating a semicircle about its diameter is:

Sphere
Cone
Cylinder
Cube
Rotation of semicircle gives a sphere.

Q25. Which chapter deals with mensuration of solids?

Circles
Surface Areas and Volumes
Triangles
Statistics
Chapter 12 focuses on surface areas and volumes.

Q26. The volume of a cube of side a is:

a3
6a2
a2
3a
Volume = side³.

Q27. The curved surface area of a cuboid is:

2(lb + bh)
2(lb + lh + bh)
2h(l + b)
lb
CSA = 2h(l + b).

Q28. The total surface area of a cuboid is:

2lb
2(lb + bh + lh)
4lh
lh
TSA = 2(lb + bh + lh).

Q29. Which solid has both curved and flat surfaces?

Cylinder
Sphere
Cube
Cuboid
Cylinder has curved surface and two flat bases.

Q30. The base radius of a cone is 7 cm and height is 24 cm. Its slant height is:

25 cm
17 cm
23 cm
25 cm
l = √(7² + 24²) = 25 cm.

Q31. Volume of a cone is one-third of:

Cylinder
Cylinder with same base and height
Sphere
Cube
Cone volume is one-third of corresponding cylinder.

Q32. If the radius of a sphere is halved, its volume becomes:

Half
One-fourth
One-eighth
Same
Volume ∝ r³.

Q33. The curved surface area of a sphere is:

Same as its total surface area
Half of TSA
Double of TSA
Zero
Sphere has no flat surface.

Q34. The radius of a sphere whose volume is 36π cm³ is:

2 cm
3 cm
4 cm
6 cm
(4/3)πr³ = 36π ⇒ r = 3 cm.

Q35. The height of a cone is perpendicular to:

Slant height
Edge
Curved surface
Base
Height is perpendicular to base.

Q36. Which solid has maximum surface area for a given volume?

Cube
Sphere
Cone
Cylinder
Cube has maximum surface area for given volume.

Q37. The slant height of a cone depends on:

Only radius
Radius and height
Only height
Diameter
l = √(r² + h²).

Q38. The curved surface area of a cylinder depends on:

Radius only
Height only
Radius and height
Diameter only
CSA = 2πrh.

Q39. A solid having all faces equal squares is:

Cube
Cuboid
Cylinder
Cone
Cube has six equal square faces.

Q40. The volume of a cylinder varies directly with:

Radius
Height
Radius + height
Square of radius
Volume = πr²h.

Q41. The total surface area of a cone is:

πr²
πr(l + r)
2πrl
πrl
TSA of cone = πr(l + r).

Q42. The shape obtained by rotating a rectangle about one of its sides is:

Cone
Sphere
Cylinder
Cube
Rotation gives a cylinder.

Q43. The volume of a hemisphere is:

(2/3)πr³
(4/3)πr³
πr³
(1/3)πr³
Volume of hemisphere = (2/3)πr³.

Q44. The base of a cylinder is:

Square
Circle
Rectangle
Triangle
Cylinder has circular base.

Q45. The unit of surface area is:

cm
cm³
cm²
m³
Surface area is measured in square units.

Q46. A sphere has:

Only curved surface
Only flat surface
Both flat and curved
Edges
Sphere has no flat surface.

Q47. The radius of a sphere whose surface area is 616 cm² is:

7 cm
14 cm
21 cm
28 cm
4πr² = 616 ⇒ r = 14 cm.

Q48. Which solid has minimum surface area for given volume?

Cube
Cylinder
Sphere
Cone
Sphere has minimum surface area.

Q49. The curved surface area of a hemisphere is:

πr²
3πr²
4πr²
2πr²
CSA of hemisphere = 2πr².

Q50. Chapter 12 mainly deals with:

Mensuration of solids
Statistics
Algebra
Trigonometry
Chapter focuses on surface areas and volumes.
NCERT Class 10 Maths Chapter 12 Surface Areas and Volumes questions covering cube, cuboid, cylinder, cone, sphere and hemisphere.
Disclaimer: We are not affiliated with NCERT. Although every care has been taken in creating this test, in case of any confusion, students should consider the NCERT textbooks and the opinion of their subject teacher as final.

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