1. 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

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

3. 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) \(2:1\)

4. 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) \(1:\sqrt2\)

5. 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

6. 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

7. 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

8. 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.

9. 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

10. 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

11. 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?

12. 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

13. 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?

14. 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

15. 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.

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

17. If the volumes of two cones are in the ratio \(1:4\) and their radii are in the ratio \(4:5\), then what will be the ratio of their heights?

(a) 1:5 (b) 5:4 (c) 5:16 (d) None of the above

18. 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.

19. If a hemisphere and a cone have equal base areas and equal heights, then what will be the ratio of their volumes?

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

20. 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

21. 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?

22. Two friends start a partnership business by investing ₹40,000 and ₹50,000 respectively. They agree that 50% of the profit will be shared equally, and the remaining 50% will be divided in the ratio of their investments. If the first friend’s share of the profit is ₹800 less than the second friend’s share, then what is the first friend’s profit?

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

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, then the ratio of their volumes will be 27:30.

25. 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?

26. 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.

27. If the volumes of two solid spheres are in the ratio 27:8, what will be the ratio of their curved surface areas?

(a) 1:2 (b) 9:4 (c) 1:8 (d) 1:16

28. If the ratio of the total surface areas of two solid spheres is 1:4, what will be the ratio of their volumes? Calculate and write it down.

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 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 ______.