1. If the surface area of a solid sphere is \(S\), and its volume is \(V\), then find the value of \(\cfrac{S^3}{V^2}\), without substituting the value of \(\pi\).

2. If the curved surface area of a right circular cylinder is \(c\) square units, the radius of the base is \(r\) units, and the volume is \(v\) cubic units, then find the value of \(\frac{cr}{v}\).

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

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

5. If the curved surface area of a solid hemisphere is \( S \) and its volume is \( V \), find the value of \( \cfrac{S^3}{V^2} \).

6. 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?

7. If the curved surface area of a right circular cylinder is \(c\) square units, the radius of the base is \(r\) units, and the volume is \(v\) cubic units, then find the value of \(\cfrac{cr}{v}\).

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

9. 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

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

11. 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 \(V\).

12. The volume of a right circular cone is \(V\) cubic units. If the area of the base is \(A\) square units and the height is \(H\) units, then find the value of \(\frac{AH}{V}\).

13. If the volume of a right circular cone is \(V\), the area of its base is \(A\), and its height is \(H\), then find the value of \(\left(\frac{AH}{V}\right)^2\).

(a) 1 (b) 4 (c) 9 (d) 3

14. 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.

15. If the curved surface area of a solid sphere is numerically equal to three times its volume, then the numerical value of the diameter of the sphere is —.

(a) 1 units (b) 2 units (c) 3 units (d) 4 units

16. If the curved surface area of a right circular cylinder is \( a \) square units, the radius of its base is \( r \) units, and the volume is \( v \) cubic units, then determine the value of \( \cfrac{ar}{v} \).

17. If the curved surface area of a right circular cylinder is \(S\), its volume is \(V\), and its radius is \(r\), then the value of \(\cfrac{Sr}{V}\) is -

(a) 2 (b) 4 (c) 8 (d) none of the above

18. 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

19. If the curved surface area of a right circular cylinder is \(C\) square units, the radius of the base is \(r\) units, and the volume is \(V\) cubic units, then determine the value of \(\cfrac{Cr}{V}\).

20. 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.

21. 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.

22. 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.

23. If the height of a right circular cylinder is 14 cm and its curved surface area is 264 square cm, then find its volume.

24. If the volume of a right circular cone is \(V\) cubic units, the area of its base is \(A\) square units, and its height is \(H\) units, then find the value of \(\frac{AH}{V}\).

25. 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.

26. 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.

27. 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 \(π\)).

28. If the curved surface area of a right circular cylinder is \(c\) square units, the base radius is \(r\) units, and the volume is \(v\) cubic units, then the value of \(\frac{cr}{v}\) is = _____.

29. 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

30. If the total surface area of a sphere is \( A \) and its volume is \( V \), what is the relationship between them ?

(a) \(A^3=36πV^2\) (b) \(A^3=36V^3 \) (c) \(A^2=4V^2\) (d) \(A=3V\)