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

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

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

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

5. 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?

6. 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.

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

8. 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.

9. 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.

10. 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.

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

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

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

14. 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

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

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

17. 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.

18. 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.

19. Find the total surface area of a solid hemisphere with radius \(x\) units.

20. The volume and total surface area of a solid hemisphere are numerically equal. Then the diameter of the hemisphere will be –

(a) 4:5 units (b) 6 units (c) 9 units (d) 3 units

21. 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?

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

23. 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.

24. 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.

25. 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.

26. 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.

27. A solid sphere has a total surface area of 1386 cm². It is melted and reshaped into several right circular cones, each with a radius of 3.5 cm and a height of 6 cm. Find the radius of the solid sphere and determine how many such cones are formed.

28. If the numerical values of the curved surface area and the total surface area of a sphere are equal, what is its radius?

(a) 3 units (b) 4 units (c) 5 units (d) 6 units

29. Two solid spheres with radii of 1 cm and 6 cm are melted and recast into a hollow sphere with a thickness of 1 cm. Find the outer radius of the new hollow sphere and calculate its curved surface area.

30. If the total surface area of a hemisphere is \(36\pi\) square centimeters, then its radius will be 3 cm.