1. If the numerical values of the volume and curved surface area of a sphere are equal, then its radius is _____ units.

2. If the radius of a right circular cylinder is 2 units, then for any height, the numerical values of the cylinder’s volume and curved surface area will be equal.

3. If the volume and curved surface area of a right circular cylinder are numerically equal, then the radius of its base will be 1 unit.

4. If the radius of a right circular cylinder is 2 units, then for any height, the numerical values of the cylinder’s volume and its curved surface area will be equal.

5. If a right circular cone and a sphere have the same radius, and the numerical value of the cone's volume is equal to the numerical value of the sphere's curved surface area, then what is the height of the cone?

(a) 10 units (b) 11 units (c) 12 units (d) 13 units

6. If the total surface area and the volume of a cube are numerically equal, then the length of its edge will be -- units.

7. If the numerical values of the volume and lateral surface area of a cone are equal, then the relationship between its height and base radius is?

(a) \(r^2-h^2=2^2\) (b) \(2r^2+h^2=3^2\) (c) \(r^2+h^2=3^2\) (d) none of the above

8. If the curved surface area of a solid sphere and three times its volume are numerically equal, then the diameter of the sphere is _____ units.

9. If the numerical values of the volume and the curved surface area of a right circular cylinder are equal, then the diameter of the cylinder is ___________ units.

10. If the numerical value of the volume and the surface area of a sphere are equal, what is the numerical value of the radius of the sphere?

(a) 3 (b) 5 (c) 7 (d) 4

11. If the numerical values of the curved surface area and the total surface area of a sphere are equal, what is its radius?

(a) 3 units (b) 4 units (c) 5 units (d) 6 units

12. If the numerical value of the volume and the curved surface area of a right circular cone are equal, find the length of the diameter of the cone — in units.

13. If the volume and curved surface area of a sphere are numerically equal, what is its radius?

(a) 5 units (b) 3 units (c) 2 units (d) 7 units

14. If the curved surface area of a solid sphere is \(s\) and its volume is \(v\), then what is the value of \(\frac{s^3}{v^2}\)?

15. If the numerical values of the volume and surface area of a solid sphere are equal, then what is the numerical value of its diameter?

16. If the radius of a right circular cylinder is 2 units, then for any height of the cylinder, the numerical values of its volume and curved surface area are equal.

17. If the radius of a right circular cylinder is 2 units, then for any height of the cylinder, the numerical values of its volume and curved surface area are equal.

18. If the curved surface area of a solid sphere is \(S\) and the volume is \(V\), then write the value of \( \cfrac{S^3}{V^2} \) (without substituting the value of \(π\)).

19. The volume and total surface area of a solid hemisphere are numerically equal. Then the diameter of the hemisphere will be –

(a) 4:5 units (b) 6 units (c) 9 units (d) 3 units

20. If a sphere's volume and surface area have equal numerical values, then the numerical value of its radius is ——.

21. If the base radius of a right circular cone is 3 cm and the height is 4 cm, then the lateral surface area of the cone will be.

(a) \(10\pi \, cm^2\) (b) \(15\pi \, cm^2\) (c) \(12\pi \, cm^2\) (d) \(18\pi \, cm^2\)

22. If \(S\) is the curved surface area and \(V\) is the volume of a sphere, the value of \(\cfrac{S^3}{V^2}\) is –

(a) 4π (b) 12π (c) 36π (d) 72π

23. If the ratio of the radii of two vertical solid circular cylinders is 2:3, and the ratio of their heights is 5:3, then the ratio of their curved surface areas will be –

(a) 2:5 (b) 8:7 (c) 10:9 (d) 16:9

24. The numerical value of a sphere’s volume and surface area are equal. What is the numerical value of the sphere’s radius?

(a) 2 (b) 3 (c) 4 (d) 5

25. The numerical value of the volume and the total surface area of a solid hemisphere are equal. Find the radius of the hemisphere.

26. If the curved surface area of a sphere is \(S\) square units and its volume is \(V\) cubic units, then determine the relationship between \(S\) and \(V\).

27. If the surface area of a sphere is \(A\) and its volume is \(V\), then find the value of \(\cfrac{A^3}{V^2}\).

28. If the total surface area of a hemisphere is \(36\pi\) square centimeters, then its radius will be 3 cm.

29. The diameter of one sphere is twice the diameter of another sphere. If the numerical value of the surface area of the larger sphere is equal to the numerical value of the volume of the smaller sphere, then what is the radius of the smaller sphere?

30. If \(h\), \(s\), and \(v\) represent the height, curved surface area, and volume of a right circular cone respectively, then the value of \(3πVh^3 – s^2h^2 + 9V^2\).

(a) 16\(\pi\) (b) 0 (c) 4\(\pi\) (d) 32\(\pi^2\)