1. Determine the ratio of the volumes of a solid right circular cylinder, a solid right circular cone, and a solid sphere — all having the same diameter and the same height.

2. Write the ratio of the volumes of a solid right circular cylinder, a solid right circular cone, and a solid sphere, all having the same diameter and the same height.

3. What is the ratio of the volumes of a solid right circular cylinder, a solid right circular cone, and a solid sphere, all having the same diameter and the same height?

4. What is the ratio of the volumes of a solid right circular cylinder, a solid right circular cone, and a solid sphere, all having the same diameter and height?

5. 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.

6. 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.

7. What is the ratio of the volumes of a right circular cylinder and a cone having the same radius and height?

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

8. 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) \(1:\sqrt2\)

9. 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.

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

11. If a solid sphere and a solid right circular cylinder have equal radii and the same volume, then calculate and write the ratio of the radius to the height of the cylinder.

12. A solid right circular cone is melted and recast into a solid right circular cylinder. The radius of both the cone and the cylinder is the same. If the height of the cone is 15 cm, calculate and write the height of the cylinder.

13. 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

14. 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) \(2 : 3\)

15. A right circular drum has a radius of 21 cm and a height of 2i. A solid iron sphere has a diameter of 21 cm. Determine the ratio of the volumes of the drum and the solid iron sphere (neglecting the thickness of the drum). Now, if the drum is completely filled with water and the sphere is fully submerged and then removed, determine the new depth of the water in the drum.

16. 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.

17. 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

18. 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

19. The curved surface area of a solid sphere is equal to the curved surface area of a solid right circular cylinder. The height and diameter of the cylinder are both 12 cm. Write the radius of the sphere.

20. The height of a solid right circular cone is 20 cm and its slant height is 25 cm. If a solid right circular cylinder of height 15 cm has the same volume as the cone, then calculate and write the diameter of the base of the cylinder.

21. A solid right circular cone is melted and recast into a solid right circular cylinder with the same radius and a height of 5 cm. Find the height of the cone.

(a) 10 cm (b) 15 cm (c) 18 cm (d) 24cm

22. The base radius of a solid right circular cone is \(r\) units, its vertical height is \(h\) units, and its slant height is \(l\) units. The cone’s base is attached to the base of a solid right circular cylinder. If the base radius and height of the cylinder are equal to those of the cone, then the total surface area of the combined solid is \((πrl + 2πrh + 2πr^2)\) square units.

23. 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.

24. What is the ratio of the volumes of a solid right circular cone and a solid sphere that can be carved with minimal wood wastage from two solid cubes, each having edge length \(a\)?

25. A hollow metallic sphere has an inner radius of 3 cm and an outer radius of 5 cm. It is melted to form a solid right circular cylinder of height \(\frac{8}{3}\) cm. Find the diameter of the base of the cylinder.

26. A sphere and a right circular cylinder both have a radius of 3 cm. If their volumes are equal, what is the height of the cylinder?

27. 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?

28. 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.

29. 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

30. The English translation is: "A solid gold sphere with a radius of 4.2 cm is melted and recast into a solid right circular cylinder with a radius of 2.8 cm. Determine the height (length) of the cylinder."