1. 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

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

3. 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

4. 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

5. 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.

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 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

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. 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.

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 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

13. 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

14. 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) \(2:1\)

15. 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.

16. 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?

17. 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?

18. 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.

19. 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?

20. 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.

21. 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

22. In a joint business, if 6 times A's capital, 8 times B's capital, and 10 times C's capital are all equal, then what will be the ratio of their capitals?

(a) 15 : 20 : 12 (b) 20 : 12 : 15 (c) 20 : 15 : 12 (d) 15 : 12 : 17

23. In a business, if two individuals invest \(x\) rupees and \(y\) rupees for 9 months and 6 months respectively, then their profit share ratio will be?

(a) \(2x:3y\) (b) \(3x:2y\) (c) \(x:y\) (d) \(2y:5x\)

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. 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 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) \(1:\sqrt2\)

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

28. 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.

29. 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.

30. 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