1. What is the ratio of the volumes of a solid right circular cylinder, a solid right circular cone, and a solid sphere, all having the same diameter and the same height?

2. What is the ratio of the volumes of a solid right circular cylinder, a solid right circular cone, and a solid sphere, all having the same diameter and height?

3. Determine the ratio of the volumes of a solid right circular cylinder and a solid right circular cone, both having the same radius and height.

4. Determine the ratio of the volumes of a solid right circular cylinder, a solid right circular cone, and a solid sphere — all having the same diameter and the same height.

5. If a solid cone and a solid right circular cylinder have the same base radius and same height, and the ratio of their curved surface areas is 5:8, then determine the ratio of their base radius to height.

6. Write the ratio of the volumes of a solid right circular cylinder, a solid right circular cone, and a solid sphere, all having the same diameter and the same height.

7. A right circular cylinder and a cone have equal bases, and the ratio of their volumes is 3:2. Prove that the height of the cone is half the height of the cylinder.

8. A solid right circular cone and a solid sphere have the same radius and the same volume. What is the ratio of the diameter of the sphere to the height of the cone?

(a) \(2 : 1 \) (b) \(1 : 2\) (c) \(1 : 1\) (d) \(2 : 3\)

9. The ratio of the base radii of a right circular cylinder and a right circular cone is 3:4, and the ratio of their heights is 2:3. What will be the ratio of the volumes of the cylinder and the cone?

10. If the volumes of two solid right circular cylinders are equal and their height ratio is 1:4, then their radius ratio will be—.

(a) \(2:1\) (b) \(\sqrt2:1\) (c) \(1:2\) (d) \(1:\sqrt2\)

11. A solid hemisphere and a solid right circular cylinder have the same height and the same base radius. Determine the ratio of their curved surface areas.

12. A right circular cylinder with the same radius and height has a volume that is three times the volume of a right circular cone.

13. If the volumes of two solid right circular cylinders are equal and their height ratio is 1:2, then their radius ratio will be –?

14. A solid right circular cone is melted and recast into a solid right circular cylinder with the same radius and a height of 5 cm. Find the height of the cone.

(a) 10 cm (b) 15 cm (c) 18 cm (d) 24cm

15. A solid right circular cone is melted and recast into a solid right circular cylinder. The radius of both the cone and the cylinder is the same. If the height of the cone is 15 cm, calculate and write the height of the cylinder.

16. A right circular cylinder and a right circular cone have equal base radii and equal heights. The ratio of their volumes is _________.

17. "A right circular cylinder and a right circular cone have a base radius ratio of 3:4 and a height ratio of 2:3; write the ratio of their volumes."

18. What is the ratio of the volumes of a solid right circular cone and a solid sphere that can be carved with minimal wood wastage from two solid cubes, each having edge length \(a\)?

19. 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

20. The ratio of the base radii of two right circular cones is 2 : 3, and the ratio of their heights is 3 : 2. Then the ratio of their volumes is —

(a) 3:2 (b) 9:4 (c) 4:9 (d) 2:3

21. A sphere and a right circular cone have the same radius \(r\) and equal volume. What is the height of the cone?

(a) \(\cfrac{r}{3}\) (b) \(\cfrac{r}{4}\) (c) \(\cfrac{3r}{4}\) (d) \(\cfrac{4r}{3}\)

22. A solid hemisphere and a solid cone have the same base radius and height. What is the ratio of their volumes?

(a) 3:2 (b) 1:3 (c) 2:3 (d) None of the above

23. If the ratio of the heights of two right circular cylinders is 1:2 and the ratio of their base circumferences is 3:4, then the ratio of their volumes will be 9:32.

24. A right circular cone and a right circular cylinder with the same base and the same height will have a volume ratio of 1 : 3.

25. If the radius of the base of a right circular cone is halved and its height is doubled, the volume of the cone remains the same.

26. A right circular cone and a hemisphere have equal base areas and volumes. Determine the ratio of their heights.

27. A right circular cylinder and a right circular cone have equal base radii and equal heights. The ratio of their volumes = ___________.

28. If the ratio of the heights of two right circular cones is 1:4 and the ratio of their radii is 2:1, then the ratio of their volumes will be ______.

29. A sphere and a right circular cylinder both have a radius of 3 cm. If their volumes are equal, what is the height of the cylinder?

30. If a solid hemisphere and a solid cone have the same base radius and height, what is the ratio of their volumes?

(a) 3:2 (b) 1:3 (c) 2:3 (d) None of the above