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

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. The numerical value of the volume and the lateral surface area of a right circular cone are equal. If the height of the cone is \( h \) and the radius is \( r \), determine the value of \(\cfrac{1}{h^2}+\cfrac{1}{r^2}\).

4. 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.

5. 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.

6. 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.

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

8. 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

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. 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

11. The numerical value of the volume and the lateral surface area of a right circular cone are equal. If the height and radius of the cone are \( h \) units and \( r \) units respectively, find the value of \[ \left( \frac{1}{h^2} + \frac{1}{r^2} \right) \]

12. The volume and the lateral surface area of a right circular cone are numerically equal. If the height and radius of the cone are \(h\) and \(r\) units respectively, write the value of \(\frac{1}{h^2} + \frac{1}{r^2}\).

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

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 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 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.

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

18. 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.

19. 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?

20. If the numerical value of the volume of a right circular cone is equal to the numerical value of its curved surface area, what is the radius of the cone?

21. The total surface area and volume of a solid hemisphere are numerically equal. Find the radius of the base of the hemisphere.

22. 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

23. The numerical values of the circumference and the area of a circular region are equal. The length of the diagonal of the square circumscribed about that circle is —

(a) 4 units (b) 2units (c) \(4\sqrt{2}\) units (d) \(2\sqrt{2}\) units

24. 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

25. The numerical value of the volume of a cube is equal to the numerical value of the sum of its edges. The total surface area of the cube is - -

(a) 12 square unit (b) 36 square unit (c) 72 square unit (d) 144 square unit

26. The diameter of one sphere is twice the diameter of another sphere. The numerical value of the curved surface area of the first sphere is equal to the numerical value of the volume of the second sphere. The numerical value of the diameter of the first sphere is...

(a) 12 units (b) 24 units (c) 48 units (d) 36 units

27. If the total surface area and the volume of a cube have the same numerical value, determine the length of its diagonal.

28. If the numerical value of the curved surface area of a sphere is equal to the numerical value of its volume, determine its radius.

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

30. "When a right circular cone has equal numerical values for its volume and lateral surface area, and its height and radius are \(h\) units and \(r\) units respectively, write the value of \(\frac{1}{h^2} +\frac{1}{r^2}\)."