1. 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.

2. 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?

3. 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?

4. 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.

5. 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.

6. 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.

7. The numerical value of the volume and the total surface area of a solid hemisphere are equal. Find the radius of the hemisphere.

8. 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

9. The total surface area and volume of a solid hemisphere are numerically equal. Find the radius of the base of the hemisphere.

10. 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

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

12. 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

13. The numerical value of the volume and the total surface area of a solid hemisphere are equal. Write the radius of the hemisphere.

14. The total surface area of a solid hemisphere is equal to the curved surface area of a solid sphere. Write the ratio of the radii of the hemisphere and the sphere.

15. If the ratio of the total surface areas of two solid spheres is 1:4, what will be the ratio of their volumes? Calculate and write it down.

16. 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.

17. 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.

18. If the ratio of the volume to the total surface area of a solid hemisphere is 4:9, what is the radius of the hemisphere?

19. 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.

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

21. If the ratio of the total surface areas of two solid spheres is 1:4, what is the ratio of their volumes?

22. 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) \(2 : 3\)

23. The ratio of the total surface area of a sphere and a hemisphere with a unit radius will be 4:3.

24. If a solid hemisphere has a radius of \(2r\) units, then its total surface area is ____ \(\pi r^2\) square units.

25. If the radius of a solid hemisphere is \(3r\) units, then its total surface area is _____.

26. The ratio of the total surface area to the curved surface area of a solid hemisphere will be –.

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

27. The ratio of the curved surface area to the total surface area of a solid hemisphere is _____.

28. The curved surface area and the total surface area of a solid hemisphere are equal.

29. If the radius of a solid hemisphere is 2r units, then the total surface area is _______ \( πr^2 \) square units.

30. Two identical solid hemispheres, each with a base radius of \(r\) units, are joined together along their flat surfaces. The total surface area of the resulting solid body will be \(6πr^3\) square units.