1. 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

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

3. 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.

4. 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

5. 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?

6. 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

7. 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) \(2:1\)

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

9. 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.

10. 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.

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

12. 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.

13. 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

14. 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?

15. 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

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

17. The radius of a hemisphere and the height of a cone are equal. If their volumes are numerically equal, then what is the ratio of the radius of the hemisphere to the radius of the cone?

18. 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

19. 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.

20. 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.

21. 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

22. A solid right circular cylinder and two hemispheres have equal base radii. If the two hemispheres are attached to the flat circular ends of the cylinder, then the total surface area of the resulting solid = curved surface area of one hemisphere + curved surface area of the cylinder + curved surface area of the other hemisphere.

23. If two triangles have their bases on the same straight line and share the same vertex (the opposite vertex), then the ratio of their areas is equal to the ratio of the lengths of their bases.

24. If a right circular cone and a hemisphere have equal volumes and equal bases, then their height ratio will be 2:1.

25. 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.

26. The total surface area of a solid hemisphere and the curved surface area of a solid sphere are equal. What is the ratio of the radius of the hemisphere to the radius of the sphere?

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

28. A right circular cylinder and a cone have equal bases, and the ratio of their volumes is 3:2. Prove that the height of the cone is half the height of the cylinder.

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

30. 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) \(1:\sqrt2\)