1. The sum of the lengths of the edges of a solid cube is 36 cm. Find the volume of the cube.

2. If the sum of the lengths of the edges of a cube is 60 cm, calculate and write the volume of the cube.

3. The volume of a sphere is directly proportional to the cube of its radius. A lead sphere has a radius of 14 cm. Using the concept of proportion, prove that this sphere can be melted to form four spheres, each with a radius of 7 cm. (Assume that the volume remains constant during melting.)

4. The numerical value of the volume of a cube is equal to the numerical value of the sum of its edges. The total surface area of the cube is - -

(a) 12 square unit (b) 36 square unit (c) 72 square unit (d) 144 square unit

5. The sum of the edge lengths of a solid cube is 36 cm. Find the volume of the cube.

(a) 27 cubic cm (b) 36 cubic cm (c) 9 cubic cm (d) 54 cubic cm

6. The maximum length of a rod that can be placed inside a cube is \(6\sqrt3\) cm. What is the volume of the cube?

7. A cube can accommodate a longest diagonal of \(6\sqrt{3}\) cm. What is the volume of the cube?

8. The sum of the lengths of the edges of a solid cube is 36 cm; the volume of the cube –

(a) 27cm\(^3\) (b) 36cm\(^3\) (c) 9cm\(^3\) (d) 54cm\(^3\)

9. The cube whose total edge length is 60 cm has a volume of —

(a) 110 cubic cm (b) 120 cubic cm (c) 125 cubic cm (d) 130 cubic cm

10. Each edge of a cube is reduced by 50%. What is the ratio of the volume of the original cube to that of the reduced cube?

11. A rod of length \(6\sqrt{3}\) cm can be placed inside a cube along its longest diagonal. What is the volume of the cube?

12. A sphere is perfectly enclosed within a cube. What is the ratio of the volume of the sphere to the volume of the cube?

13. If the area of one face of a cube is 4 times the area of a face of another cube, then how many times is the volume of the first cube compared to the volume of the second cube?

14. A rectangular container has a base in the shape of a rectangle with a length of 60 cm and a width of 45 cm. The container has a height of 20 cm and is half-filled with water. Determine the side length of a metallic cube that, when placed in the container, will cause the water level to reach the brim.

15. The volume of a rectangular prism is 432 cubic cm. If two equal-sized cubes are created from it, determine the edge length of each cube.

16. If the total length of the edges of a solid cube is 36 cm, then its volume will be –?

(a) 9 cubic cm (b) 54 cubic cm (c) 27 cubic cm (d) 36 cubic cm

17. The lateral surface area of a cube is 256 square meters. What is the volume of the cube?

(a) 64 cubic m. (b) 216 cubic m. (c) 256 cubic m (d) 512 cubic m

18. "The volume of a sphere is directly proportional to the cube of its radius. Three solid spheres with diameters of 1½, 2, and 2½ meters are melted to form a new solid sphere. Find the diameter of the new sphere. (Assume volume remains the same before and after melting.)

19. A rod of length \( 4\sqrt{3} \) cm is placed inside a cube along its longest diagonal. What is the volume of the cube?

20. The total surface area of a cube is 216 square centimeters. Find the volume of the cube.

21. The ratio of the volumes of two cubes is 4:125. What is the ratio of the surface areas of the two cubes?

(a) 2:5 (b) 4:25 (c) 4:5 (d) 2:25

22. The volume ratio of a sphere and the circumscribed cube of the sphere is

(a) π:2 (b) π:3 (c) π:4 (d) π:6

23. 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

24. The volume of a cube is equal to the area of one of its faces. What is the length of its edge?

(a) 4 units (b) 5 units (c) 6 units (d) 8 units

25. The outer and inner radii of a hollow cylinder are 11 cm and 10 cm respectively, and its height is 14 cm. What is the volume of the metallic part of the cylinder?

(a) 880 cubic cm (b) 968 cubic cm (c) 88 cubic cm (d) 924 cubic cm

26. If each face diagonal of a cube is \(8\sqrt{2}\) cm long, then what is the length of the space diagonal of the cube?

(a) \(8\sqrt3\) cm (b) \(3\sqrt8\) cm (c) \(3\sqrt2\) cm (d) \(2\sqrt3\) cm

27. What is the volume of the largest cube that can be cut out from a sphere with radius \(4\sqrt{3}\) cm?

(a) 512 cubic cm (b) 64 cubic cm (c) 216 cubic cm (d) 729 cubic cm

28. If the total surface area of a cube is 216 square centimeters, what is its volume?

(a) 216 tcubic cm (b) 212 cubic cm (c) 316 cubic cm (d) 256

29. If the length of the diagonal of a cube is \(\sqrt{12}\) cm, what is its volume?

(a) 18 cubic cm (b) 8 cubic cm (c) 6 cubic cm (d) 16 cubic cm

30. The sum of the length, width, and height of a rectangular box is 24 cm, and the length of its diagonal is 15 cm. What is the total surface area of the rectangular box?

(a) 360 square cm (b) 221 square cm (c) 351quare cm (d) 256 quare cm