1. 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

2. 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?

3. From a cuboid measuring 16 cm × 4 cm × 2 cm, several cubes with edge length 2 cm are cut out. What is the ratio of the total surface area of the original cuboid to the total surface area of all the cubes?

(a) 11:48 (b) 12:50 (c) 13:36 (d) 14:28

4. If the length of each face diagonal of a cube is \(5\sqrt{2}\) cm, then what is the length of the space diagonal of the cube?

(a) \(3\sqrt5\) cm (b) \(4\sqrt3\) (c) \(5\sqrt3\) (d) \(6\sqrt3\)

5. If the length of each edge of a cube is doubled, then by what percentage will the total surface area of the cube increase?

6. If the length of a cube's diagonal is \(4\sqrt{3}\) cm, determine its total surface area.

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. If the length of the diagonal of a cube is \(4\sqrt{3}\) cm, determine the total surface area of the cube.

9. If the length of a diagonal of a cube is \(4\sqrt{3}\) cm, calculate and write the total surface area of the cube.

10. If the total surface area of a cube is \(s\) square units and the length of its diagonal is \(d\) units, what is the relationship between \(s\) and \(d\)?

(a) s=6d\(^2\) (b) 3s=7d (c) s\(^3\)=d2\(^2\) (d) d\(^2\)=s/2

11. 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

12. If each edge of a cube is increased by 20%, by what percentage will the total surface area increase?

(a) 40% (b) 42% (c) 44% (d) 46%

13. Let the length of each edge of the cube be \(a\) cm \(\therefore\) The total surface area of the cube = \(6a^2\) square cm If the edge length is increased by 20%, the new edge length = \(a + a \times \cfrac{20}{100}\) cm \(= a + \cfrac{a}{5} = \cfrac{6a}{5}\) cm \(\therefore\) New total surface area of the cube = \(6\left(\cfrac{6a}{5}\right)^2\) square cm = \(\cfrac{216a^2}{25}\) square cm \(\therefore\) Percentage increase in surface area \(= \cfrac{\cfrac{216a^2}{25} - 6a^2}{6a^2} \times 100\%\) \(= \cfrac{(216a^2 - 150a^2) \times 100}{25 \times 6a^2}\%\) \(= \cfrac{4 \times 66a^2}{6a^2}\%\) \(= 44\%\)

14. If the volume of a cube is \(V\) cubic centimeters, the total surface area is \(S\) square centimeters, and the length of the diagonal is \(d\) centimeters, then prove that \(Sd = 6\sqrt{3}V\).

15. A hollow vertical cylindrical iron pipe has an outer radius of 5 cm and an inner radius of 4 cm. If the total surface area of the pipe is 1188 square cm, what is the length of the pipe?

16. If the total surface area of a cube is \(s\) square units and the length of its diagonal is \(d\) units, then the relationship between \(s\) and \(d\) will be –

(a) \(s=6d^2\) (b) \(3s=7d\) (c) \(s^3=d^2\) (d) \(d^2 = \cfrac{s}{2}\)

17. If each edge of a cube is increased by 10%, by what percentage does the total surface area increase?

(a) 30.2% (b) 39.6% (c) 33.1% (d) 38.3%

18. If the total surface area of a cube is \(s\) square units and the length of its diagonal is \(d\) units, then the relationship between \(s\) and \(d\) is \[ s = 6d^2 \]

19. If the total surface area of a cube is \(s\) square units and the length of its diagonal is \(d\) units, then the relationship between \(s\) and \(d\) is \(s^3 = d^2\).

20. 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.

21. The length of a diagonal of a cube is \(4\sqrt{3}\) cm. Calculate the total surface area of the cube.

22. 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

23. 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

24. If a right circular cone has a base diameter of 7 cm and a slant height of 10 cm, what is the total surface area of the cone?

(a) 184.5 square cm (b) 185.4 square cm (c) 148.5 square cm (d) 184.6 square cm

25. 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

26. 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

27. 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.

28. If the ratio of the volumes of two cubes is 8:27, then what will be the ratio of their total surface areas?

29. A hollow cylindrical iron pipe open at both ends has an inner radius and outer radius of 4 cm and 5 cm respectively. If the total surface area of the pipe is 1188 square centimeters, what is the length of the pipe?

30. The total surface area of a right square prism is equal to half the square of its diagonal. Show that the prism is a cube.