1. 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

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

3. 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?

4. 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.

5. 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.

6. 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

7. 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) \(A=3V\)

8. 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

9. 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

10. The total surface area of a solid hemisphere and the curved surface area of a solid sphere are equal. What is the ratio of the radius of the hemisphere to the radius of the sphere?

11. A solid sphere and a solid cone have the same diameter, and their total surface areas are equal. What is the ratio of the cone's height to its diameter?

12. If the curved surface area of a right circular cylinder is 440 cm² and its volume is 1540 cm³, what is its radius?

(a) 5 cm (b) 6 cm (c) 7 cm (d) 8 cm

13. 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.

14. 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

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

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 numerical value of the curved surface area and the volume of a sphere are equal, then the radius will be 3 units.

19. 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.

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

21. The volume of a right rectangular prism is 960 cubic centimeters. If the ratio of its length, width, and height is 6:5:4, what is the total surface area of the prism?

(a) 590 square cm (b) 592 square cm (c) 295 square cm (d) 596 square cm

22. The length of a right rectangular prism is three times its width and five times its height. If its volume is 14,400 cubic centimeters, then what is its total surface area?

(a) 4300 square cm (b) 4320 square cm (c) 4500 square cm (d) 4520 square cm

23. If the total surface area of a solid sphere is 462 square centimeters, what is its diameter?

(a) 7 cm (b) 14 cm (c) 21 cm (d) 3.5 cm

24. If the radius of a sphere is increased by 2 cm, its curved surface area increases by 352 square centimeters. What was the original radius of the sphere?

(a) 5 cm (b) 6 cm (c) 7 cm (d) 5.6 cm

25. The sum of the length, width, and height of a rectangular box is 24 cm, and the length of its diagonal is 15 cm. What is the total surface area of the rectangular box?

(a) 360 square cm (b) 221 square cm (c) 351quare cm (d) 256 quare cm

26. If the length, breadth, and height of a right rectangular prism are in the ratio 3:2:1 and its total surface area is 88 square centimeters, then what is its volume?

(a) 120 cubic cm (b) 64 cubic cm (c) 48 cubic cm (d) 24 cubic cm

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

28. 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 \(V\).

29. If the curved surface area of a right circular cylinder is 264 square meters and its volume is 924 cubic meters, then what is the radius of the base?

30. 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.