1. If a solid hemisphere and a solid cone have the same base radius and height, what is the ratio of their volumes?

(a) 3:2 (b) 1:3 (c) 2:3 (d) None of the above

2. A solid hemisphere and a solid cone have the same base radius and height. Determine the ratio of their volumes.

(a) 3:2 (b) 11:3 (c) 2:3 (d) 4:3

3. 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.

4. 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.

5. A solid hemisphere and a solid right circular cylinder have the same height and the same base radius. Determine the ratio of their curved surface areas.

6. If a solid hemisphere and a solid cone have equal base areas and equal heights, then what is the ratio of their volumes?

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

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

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

9. If a solid hemisphere and a cone have the same base diameter and height, then their volume ratio is—

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

10. If a solid hemisphere and a solid cylinder have the same base radius and height, then their volume ratio will be—

(a) 4:3 (b) 2:3 (c) 11:3 (d) 3:2

11. 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.

12. 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

13. If a hemisphere and a cone have the same base area and the same height, find the ratio of their curved surface areas.

14. A solid sphere and a solid cone have the same diameter, and their total surface areas are equal. What is the ratio of the cone's height to its diameter?

15. A solid right circular cone and a solid sphere have the same radius and the same volume. What is the ratio of the diameter of the sphere to the height of the cone?

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

16. Determine the volume ratio of a solid cone, a solid hemisphere, and a solid cylinder that have equal base diameters and equal heights.

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

18. A hollow iron cylinder of height 20 cm has an outer radius of 5 cm and an inner radius of 4 cm. This cylinder is melted and recast into a solid cone whose height is one-third of the original cylinder's height. Find the diameter of the base of the cone.

19. 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.

20. A cone, a hemisphere, and a sphere have equal radius and height. Their volumes are in the ratio 1:2:3.

21. 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?

22. Determine the volume ratio of a solid cone, a solid hemisphere, and a solid cylinder with equal base diameters and equal heights.

23. If a solid sphere and a solid right circular cylinder have the same radius and equal volume, then write the ratio of the cylinder's radius to its height.

24. A solid object has its lower part in the shape of a hemisphere and its upper part in the shape of a right circular cone. If the surface areas of both parts are equal, determine the ratio of the radius to the height of the cone.

25. Determine the ratio of the volumes of a solid right circular cylinder and a solid right circular cone, both having the same radius and height.

26. The bottom part of a solid is in the shape of a hemisphere, and the top part is in the shape of a right circular cone. If the surface areas of both parts are equal, then calculate and write the ratio of the radius to the height of the cone.

27. 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.

28. The ratio of the total surface areas of a solid sphere and a solid hemisphere of the same radius is 2:1.

29. 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) \(2:1\)

30. 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