1. 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

2. 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

3. 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 \[ s = 6d^2 \]

4. 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 \(s^3 = d^2\).

5. If the total surface area of a cube is 150 square centimeters, then its volume will be 150 cubic centimeters.

6. 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."

7. 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) \(d^2 = \cfrac{s}{2}\)

8. 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.

9. 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.

10. 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.

11. The difference between the outer and inner curved surface areas of a hollow cylindrical pipe is 44 square centimeters, and the length of the pipe is 14 cm. The volume of the material of the pipe is 99 cubic centimeters. Find the outer and inner radii of the pipe.

12. 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

13. 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

14. 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.

15. If the length of one diagonal of a rhombus is three times the length of the other diagonal, and the area of the rhombus-shaped field is 96 square centimeters, then the length of the longer diagonal is –

(a) 8 cm (b) 12 cm (c) 16 cm (d) 24cm

16. 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?

17. If the total area of the 6 faces of a cube is 216 square centimeters, calculate and write the volume of the cube.

18. 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

19. If the radius of a cone is \(r\) units, the height is \(h\) units, and the curved surface area is \(S\) square units, then prove that \[ h = \frac{\sqrt{S^2 - \pi^2 r^4}}{\pi r} \]

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

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

22. 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

23. If the curved surface area of a right circular cylinder is \(c\) square units, the base radius is \(r\) units, and the volume is \(v\) cubic units, then the value of \(\frac{cr}{v}\) is = _____.

24. 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

25. In triangle \(\triangle ABC\), D and E are the midpoints of sides AB and AC respectively. If the area of triangle ABC is 36 square centimeters, then what is the area of triangle ADE?

(a) 6 square centimeters (b) 9 square centimeters (c) 12 square centimeters (d) 16 square centimeters

26. If E and F are the midpoints of sides AB and AD respectively in parallelogram ABCD, and the area of parallelogram ABCD is 1600 square centimeters, then what is the area of triangle AEF?

(a) 400 sq cm (b) 200 sq cm (c) 300 sq cm (d) None of the above

27. 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

28. 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 \(= \cfrac{\cfrac{216a^2}{25} - 6a^2}{6a^2} \times 100\%\) \(= \cfrac{(216a^2 - 150a^2) \times 100}{25 \times 6a^2}\%\) \(= \cfrac{4 \times 66a^2}{6a^2}\%\) \(= 44\%\)

29. The curved surface area of a right circular cylinder is 440 square centimeters. If the height of the cylinder is 10 centimeters, find its volume.

30. If the curved surface area of a sphere is \(S\) square units and its volume is \(V\) cubic units, then determine the relationship between \(S\) and \(V\).