1. If the volume of a solid hemisphere is \(144\pi\) cubic cm, what is its total surface area?

2. 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?

3. The length of a right rectangular prism is three times its width and five times its height. If its volume is 14,400 cubic centimeters, then what is its total surface area?

(a) 4300 square cm (b) 4320 square cm (c) 4500 square cm (d) 4520 square cm

4. The diameter of one sphere is twice the diameter of another sphere. The curved surface area of the first sphere is equal to the volume of the second sphere. What is the radius of the first sphere?

(a) 21 (b) 22 (c) 23 (d) 24

5. The dimensions of a right rectangular prism are in the ratio 6:5:4. If its total surface area is 3700 square centimeters, what is its volume in cubic centimeters?

(a) 1500 cubic cm (b) 51000 cubic cm (c) 50100 cubic cm (d) 15000 cubic cm

6. If the total surface area of a solid sphere is 462 square centimeters, what is its diameter?

(a) 7 cm (b) 14 cm (c) 21 cm (d) 3.5 cm

7. A solid lead sphere with a diameter of 12 cm is melted to form three smaller spheres. If the diameters of the smaller spheres are in the ratio 3:4:5, what is the radius of the smallest sphere?

(a) 1.5 cm (b) 3 cm (c) 4 cm (d) 5 cm

8. A solid cone with a diameter of 16 cm and a height of 2 cm is melted to form 12 identical spheres. What is the diameter of each sphere?

(a) \(\sqrt3\) cm (b) 2 cm (c) 3 cm (d) 4 cm

9. 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?

10. 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?

11. 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

12. The diameter of one sphere is twice the diameter of another sphere. If the numerical value of the surface area of the larger sphere is equal to the numerical value of the volume of the smaller sphere, then what is the radius of the smaller sphere?

13. 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

14. If two solid spheres with diameters of 1 cm and 6 cm are melted and recast into a hollow sphere with a thickness of 1 cm, then what is the outer surface area of the new hollow sphere?

15. Two cubes with equal edge lengths are joined side by side to form a cuboid. If the volume of the cuboid is 1024 cubic centimeters, what is the length of each edge of the cubes?

16. 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) \(2 : 3\)

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

18. 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.

19. If the numerical values of the volume and surface area of a solid sphere are equal, then what is the numerical value of its diameter?

20. 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?

21. 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.

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

23. 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

24. 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

25. If a solid hemisphere has a total surface area of \(108\pi \, \text{cm}^2\), then what is its volume?

26. If the numerical value of the volume and the surface area of a sphere are equal, what is the numerical value of the radius of the sphere?

(a) 3 (b) 5 (c) 7 (d) 4

27. 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

28. The volume of the largest solid cone that can be cut out from a solid hemisphere with a radius of r units.

(a) \(4\pi r^3\) cubic units. (b) \(43\pi r^3\) cubic units. (c) \(\cfrac{πr^3}{4} \)  cubic units (d) \(\cfrac{πr^3}{3}\) cubic units

29. 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

30. The volume of a right rectangular prism is 960 cubic centimeters. If the ratio of its length, width, and height is 6:5:4, what is the total surface area of the prism?

(a) 590 square cm (b) 592 square cm (c) 295 square cm (d) 596 square cm