1. If the length, breadth, and height of a right rectangular prism are in the ratio 3:2:1 and its total surface area is 88 square centimeters, then what is its volume?

(a) 120 cubic cm (b) 64 cubic cm (c) 48 cubic cm (d) 24 cubic cm

2. 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

3. The length, width, and height of a rectangular prism are in the ratio 5:3:1. If the volume of the prism is 120 cubic centimeters, determine the total surface area.

4. A rectangular box has a length, width, and height ratio of 3:2:1. If its volume is 384 cubic centimeters, find the total surface area of the box.

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. A rectangular box has its length, breadth, and height in the ratio 3:2:1, and its volume is 384 cubic centimeters. Find the surface area of the box.

7. In a rectangular prism, the ratio of length, width, and height is \(4:5:3\). If the length of one diagonal is \(35\sqrt2\) cm, what is the total surface area?

8. The sum of the length, width, and height of a right rectangular prism is 25 cm, and its total surface area is 264 square cm. Determine the length of its diagonal.

9. If the length, breadth, and height of a rectangular box are in the ratio 3:2:1 and its volume is 384 cubic centimeters, calculate and write the total surface area of the box.

10. 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

11. Here’s the English translation of your sentence: "A right rectangular prism has its length twice the breadth and its height half the breadth. If the total surface area of the prism is 448 square centimeters, find its volume."

12. A solid cuboid has a length, width, and height ratio of \(4:3:2\), and its total surface area is \(468\) square cm. Determine the volume of the cuboid.

13. The diagonal of a cuboid is √725 cm and its volume is 3000 cubic cm. The total surface area of the cuboid is 1300 square cm. Find the length, breadth, and height of the cuboid.

14. The length, breadth, and height of a cuboid are in the ratio 4:3:2. If its total surface area is 468 square meters, find the volume of the cuboid.

15. The sum of the length, breadth, 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 box?

16. The internal volume of a right-angled rectangular box is 440 cubic centimeters, and the area of its base is 88 square centimeters.
Calculate and write the internal height of the box.

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

17. A rectangular piece of soft cardboard has a length that is four times its width. When rolled along its length, it forms a right circular cone whose lateral surface area is 100 square centimeters. What is the height of the cone?

18. If the curved surface area of a right circular cylinder is 264 square meters and its volume is 924 cubic meters, then what is the radius of the base?

19. 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?

20. A right circular cylinder has a height-to-base-radius ratio of 3:1. If the volume of the cylinder is \(1029\pi\) cubic cm, find the total surface area of the cylinder.

21. If the volume of a right circular cone is \(X\) cubic units, the area of its base is \(Y\) square units, and its height is \(Z\) units, then what is the value of \(\frac{YZ}{X}\)?

22. If the height of a right circular cone is 14 cm and its curved surface area is 264 cm², what is the volume of the cone?

23. The curved surface area of a right circular cylinder is 264 square meters, and its volume is 924 cubic meters. Find the diameter and height of the cylinder.

24. The outer dimensions of a box with a lid are 12 cm in length, 10 cm in width, and 8 cm in height. The total inner surface area of the box is 376 square cm. If the walls of the box have equal thickness, what is their thickness?

25. The curved surface area of a right circular cylinder is 440 square cm, and its volume is 1540 cubic cm. Find the height of the cylinder.

26. If the curved surface area of a right circular cylindrical column is 264 square meters and its volume is 924 cubic meters, calculate the diameter and height of the column.

27. If the curved surface area of a right circular cylindrical pillar is 264 square meters and its volume is 924 cubic meters, determine the diameter and height of the pillar.

28. If the volume of a right circular cone is \(V\) cubic units, the area of the base is \(A\) square units, and the height is \(H\), then what is the value of \(\frac{AH}{V}\)?

29. If the total surface area of a sphere is \( A \) and its volume is \( V \), what is the relationship between them ?

(a) \(A^3=36πV^2\) (b) \(A^3=36V^3 \) (c) \(A^2=4V^2\) (d) \(A=3V\)

30. If the radius of a right circular cone is \(\cfrac{r}{2}\) units and the slant height is \(2l\) units, then the total surface area is –

(a) \(2πr (l+r)\) square units (b) \(πr\left(l+\cfrac{r}{4}\right)\) square units (c) \(πr(l+r)\) square units (d) \(2πr l\) square units