1. 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?

2. 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.

3. 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.

4. 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.

5. Two right circular cylinders have a height ratio of 1:2 and a base circumference ratio of 3:4. What is the ratio of their volumes?

6. The height of a solid right circular cone is 20 cm and its slant height is 25 cm. If a solid right circular cylinder of height 15 cm has the same volume as the cone, then calculate and write the diameter of the base of the cylinder.

7. "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."

8. If a right circular cone and a hemisphere have equal volumes and equal bases, then their height ratio will be 2:1.

9. If the volumes of two solid right circular cylinders are equal and their heights are in the ratio 1:2, what will be the ratio of the lengths of their radii?

(a) 1:√2 (b) √2:1 (c) 1:2 (d) 2:1

10. Two right circular cones of equal height have their base diameters in the ratio 2 : 3. The ratio of their volumes will be —

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

11. What is the ratio of the volumes of a right circular cylinder and a cone having the same radius and height?

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

12. 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?

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

14. 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 ______.

15. 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.

16. 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) \(2 : 3\)

17. 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) \(1:\sqrt2\)

18. 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.

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

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

21. If a solid sphere and a solid right circular cylinder have the same radius and equal volume, then write the ratio of the cylinder's radius to its height.

22. If the radius of the base of a right circular cone is halved and its height is doubled, the volume of the cone will remain the same.

23. 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?

24. If the ratio of the heights of two right circular cylinders is 1:2, and the ratio of the perimeters (circumferences) of their bases is 3:4, then find the ratio of their volumes.

25. 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.

26. If the heights of two right circular cylinders are in the ratio 1:2 and the circumferences of their bases are in the ratio 3:4, then what is the ratio of their volumes?

27. If the heights of two right circular cones are in the ratio 1 : 3 and the lengths of their radii are in the ratio 3 : 1 respectively, then show by calculation that the ratio of their volumes will be 3 : 1.

28. If a solid sphere and a solid right circular cylinder have equal radii and the same volume, then calculate and write the ratio of the radius to the height of the cylinder.

29. 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.

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