1. If two cones have equal base radii and their heights are in the ratio 2:3, then the ratio of their volumes will be ______.

2. 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?

3. 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

4. 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.

5. 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.

6. 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) \(1:\sqrt2\)

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

8. 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

9. 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 ______.

10. If the ratio of the radii of two solid right circular cones is 2:3 and the ratio of their heights is 5:3, then the ratio of their volumes will be 27:30.

11. 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?

12. If the ratio of the radii of two right circular cylinders is 2:3 and the ratio of their heights is 5:6, what will be the ratio of their volumes?

13. 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.

14. "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."

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

16. If two solid right circular cones have equal volume and their heights are in the ratio 1:2, then what is the ratio of the lengths of their radii?

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

17. The volumes of two perpendicular circular rings are equal. The ratio of their heights is 4:9, then what will be the ratio of their radii?

(a) 3:2 (b) 2:3 (c) 4:9 (d) 8:9

18. If the volumes of two vertical circular cylinders are equal, and their heights are in the ratio 4:9, then the ratio of their radii will be –

(a) 3:2 (b) 2:3 (c) 4:9 (d) 8:9

19. If the volumes of two vertical solid cylinders are equal, and their heights are in the ratio 1:2, then the ratio of the lengths of their radii will be –

(a) 1: √2 (b) √2:1 (c) 1:2 (d) 2:1

20. If the volumes of two right circular cylinders of equal height are in the ratio 16:25, then what is the ratio of their radii?

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

21. If the radii of two cones are in the ratio 2:3 and their heights are in the ratio 5:3, then what will be the ratio of their volumes?

(a) 4:9 (b) 9:4 (c) 27:20 (d) 20:27

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

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

24. If the ratio of the radii of two solid right circular cones is 2:3 and the ratio of their heights is 5:3, determine the ratio of their volumes.

(a) 27:20 (b) 4:9 (c) 9:4 (d) 20:27

25. 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.

26. If the volumes of two right circular solid cylinders are equal and the ratio of their heights is 1:2, then find the ratio of their radii.

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

27. 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?

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

29. If the ratio of the radii of two vertical solid circular cylinders is 2:3, and the ratio of their heights is 5:3, then the ratio of their curved surface areas will be –

(a) 2:5 (b) 8:7 (c) 10:9 (d) 16:9

30. If the volumes of two cones are in the ratio 1:4 and the ratio of the diameters of their bases is 4:5, find the ratio of their heights

(a) 1:5 (b) 5:4 (c) 5:16 (d) 25:64