1. If the ratio of the radii of two right circular solid cones is 2:3 and the ratio of their heights is 5:3, then what is the ratio of their volumes?

2. 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.

3. 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

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. If the ratio of the radii of two perpendicular solid cones is 2:3 and the ratio of their heights is 5:3, what is the ratio of their volumes ?

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

6. If the volumes of two cones are in the ratio 2:3 and the ratio of their base radii is 1:2, then what is the ratio of their heights?

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

7. 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 ______.

8. The volume of a cone is jointly proportional to the square of the radius of the base and its height. If the ratio of the radii of two cones is 2:3 and their heights are in the ratio 5:4, then find the ratio of their volumes.

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 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?

11. If the ratio of the radii of two tall solid circular cones is 2:3 and the ratio of their heights is 5:3, then what is the ratio of their curved surface areas?

(a) 8:07 (b) 2:05 (c) 10:09 (d) 16:09

12. 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.

13. The ratio of the radii of two right circular solid cylinders is 2:3, and the ratio of their heights is 5:3. Find the ratio of their curved surface areas.

14. 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?

15. The volume of a cone is jointly proportional to the square of the radius of its base and its height. If the ratio of the base radii of two cones is 2:3 and the ratio of their heights is 5:4, find the ratio of their volumes.

16. 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

17. 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.

18. 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?

19. If the height ratio of two right circular cones is 1:3 and the ratio of their radii is 3:1, then show that the ratio of their volumes is 3:1.

20. The volume of a cylinder varies jointly with the square of the radius of its base and its height. If the ratio of the base radii of two cylinders is 2:3 and the ratio of their heights is 5:4, determine the ratio of their volumes.

21. 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

22. 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) \(2:1\)

23. Two vertical cylindrical vessels have equal volumes, and the ratio of their heights is 1:2. What is the ratio of the lengths of their radii?

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

25. If the radii of two right circular solid cylinders are in the ratio 2:3 and their heights are in the ratio 5:3, then find the ratio of their volumes.

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

26. If the ratio of the radii of two vertical solid cylinders is 2:3 and the ratio of their heights is 5:3, then the ratio of their curved surface areas is 20:27.

27. 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

28. 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

29. 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

30. 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