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 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

3. 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.

4. 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?

5. 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.

6. 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

7. If the diameters of two cones are equal and the ratio of their slant heights is 5:7, then what is the ratio of their curved surface areas?

(a) 25:7 (b) 25:49 (c) 5:49 (d) 5:7

8. 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

9. 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

10. If the ratio of the curved surface areas of two hemispheres is 4:9, then the ratio of their radii will be 2:3.

11. 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

12. 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.

13. If a solid hemisphere and a solid cone have equal base diameters and equal heights, find the ratio of their curved surface areas.

14. If the ratio of the volumes of two solid spheres is 1:27, then what is the ratio of their curved surface areas?

(a) 1:9 (b) 1:4 (c) 1:3 (d) 1:2

15. If the ratio of the curved surface areas of two solid spheres is \(1:9\), then their volume ratio will be?

(a) 1:3 (b) 1:27 (c) 1:81 (d) 1:243

16. 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?

17. 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.

18. If the ratio of the volumes of two solid spheres is 1:8, then the ratio of their curved surface areas is 1:4.

19. 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

20. A solid hemisphere and a solid cone have equal base diameters and equal heights. Calculate and write the ratio of their volumes and the ratio of their curved surface areas.

21. 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.

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. The volume ratio of two solid spheres is 4:27. The ratio of their curved surface areas is-

(a) 4:9 (b) 2:3 (c) 16:35 (d) 8:27

24. If the volume ratio of two solid spheres is 1:8, the ratio of their curved surface areas will be -

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

25. 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

26. 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

27. 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.

28. 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?

29. 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 ______.

30. A solid hemisphere and a solid cone have the same base diameter and height. Determine the ratio of their volumes and the ratio of their curved surface areas.