Class 10 Mathematics (NCERT)

1. Two cubes each of volume 64 cm³ are joined end to end. The surface area of the resulting cuboid is:

• A. 160 cm²
• B. 128 cm²
• C. 144 cm²
• D. 120 cm²

2. Total surface area of a solid hemisphere of radius r is:

• A. 2πr²
• B. 3πr²
• C. 4πr²
• D. (2/3)πr³

3. Curved surface area of a right circular cone with radius r and slant height l is:

• A. πr²h
• B. πrl
• C. 2πrl
• D. πr(l + r)

4. Volume of a sphere of radius r is given by:

• A. (4/3)πr³
• B. (2/3)πr³
• C. 4πr²
• D. (1/3)πr³

5. If the radius of a sphere is doubled, then its volume becomes how many times?

• A. 2 times
• B. 4 times
• C. 8 times
• D. 16 times

6. Relationship between height (h), radius (r), and slant height (l) of a cone is:

• A. l² = h² + r²
• B. l = h + r
• C. h² = l² + r²
• D. r² = l² + h²

7. A metallic sphere of radius 3 cm is melted and recast into a wire of radius 0.2 cm. Length of wire is:

• A. 900 cm
• B. 450 cm
• C. 90 cm
• D. 360 cm

8. The curved surface area of a cylinder of radius 7 cm and height 10 cm is:

• A. 440 cm²
• B. 220 cm²
• C. 1540 cm²
• D. 880 cm²

9. If volumes of two spheres are in ratio 64 : 27, then ratio of their surface areas is:

• A. 4 : 3
• B. 16 : 9
• C. 9 : 16
• D. 3 : 4

10. Volume of a cone of height 12 cm and base radius 7 cm is:

• A. 616 cm³
• B. 1848 cm³
• C. 308 cm³
• D. 1232 cm³

11. Total surface area of a cube of edge length 'a' is:

• A. 4a²
• B. 6a²
• C. a³
• D. 12a

12. Volume of a hemisphere of radius 3 cm is:

• A. 18π cm³
• B. 36π cm³
• C. 54π cm³
• D. 9π cm³

13. Slant height of a cone having radius 5 cm and height 12 cm is:

• A. 13 cm
• B. 17 cm
• C. 15 cm
• D. 10 cm

14. Ratio of total surface area to curved surface area of a solid hemisphere is:

• A. 3 : 2
• B. 2 : 3
• C. 4 : 3
• D. 1 : 2

15. Length of diagonal of a cube of edge 'a' is:

• A. a√2
• B. a√3
• C. 2a
• D. a√6

16. If height and radius of a cone are doubled, then its volume becomes:

• A. 2 times
• B. 4 times
• C. 8 times
• D. 16 times

17. A solid piece of iron in form of a cuboid of dimensions 49cm × 33cm × 24cm is melted to form a solid sphere. Radius of sphere is:

• A. 21 cm
• B. 14 cm
• C. 28 cm
• D. 7 cm

18. The total surface area of a hollow hemisphere of outer radius R and inner radius r is:

• A. 2π(R² + r²)
• B. π(3R² + r²)
• C. 3π(R² - r²)
• D. 2π(R² - r²)

19. Total surface area of a cylinder of radius r and height h is:

• A. 2πr(r + h)
• B. 2πrh
• C. πr(r + h)
• D. 2πr²h

20. The radius of a sphere whose surface area is 154 cm² is:

• A. 3.5 cm
• B. 7 cm
• C. 14 cm
• D. 2.5 cm

21. Volume of the largest right circular cone that can be cut out of a cube of edge 7 cm is:

• A. 89.83 cm³
• B. 179.66 cm³
• C. 44.91 cm³
• D. 343 cm³

22. If radius of base of a cylinder is doubled and height is halved, its volume becomes:

• A. Same
• B. Doubled
• C. Halved
• D. Quadrupled

23. Number of spherical balls of diameter 2 cm that can be made by melting a solid sphere of radius 8 cm is:

• A. 512
• B. 64
• C. 256
• D. 128

24. Lateral surface area of a cube is 256 cm². Edge of the cube is:

• A. 8 cm
• B. 16 cm
• C. 64 cm
• D. 4 cm

25. Total surface area of a cone of base radius r and slant height l is:

• A. πr(l + r)
• B. πrl
• C. 2πr(l + r)
• D. πr²l

26. Total surface area of a solid wooden toy in the shape of a hemisphere surmounted by a cone is:

• A. πr(l + 2r)
• B. πr(l + r)
• C. 2πr(l + r)
• D. πr²(h + r)

27. Ratio of volumes of a cylinder, cone, and sphere having same radius and same height (height = diameter = 2r) is:

• A. 3 : 1 : 2
• B. 1 : 2 : 3
• C. 3 : 2 : 1
• D. 2 : 1 : 3

28. A cone and a cylinder have equal bases and equal heights. Ratio of their volumes is:

• A. 1 : 3
• B. 3 : 1
• C. 1 : 2
• D. 2 : 1

29. The capacity of a cylindrical tank of radius 2.1 m and height 5 m is:

• A. 69.3 m³
• B. 34.65 m³
• C. 138.6 m³
• D. 693 m³

30. Surface area of a sphere of diameter 14 cm is:

• A. 616 cm²
• B. 308 cm²
• C. 154 cm²
• D. 1232 cm²