1. 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

2. If a right-angled quadrilateral has \(x\) number of vertices, \(y\) number of edges, and \(z\) number of faces, then what is the value of \(x - y + z\)? (a) 8 (b) 6 (c) 2 (d) 12

3. If a right-angled quadrilateral has \(a\) number of vertices, \(b\) number of edges, and \(c\) number of faces, then what is the value of \(2a - b + 3c\)? (a) 16 (b) 18 (c) 20 (d) 22

4. If the number of vertices, faces, and edges of a cuboid are \( p \), \( q \), and \( r \) respectively, what is the value of \( \frac{3(p + r)}{2q} \) ? (a) 10 (b) 12 (c) 5 (d) 6

5. If a cuboid has \(x\) number of vertices, \(y\) number of edges, and \(z\) number of faces, then what is the value of \((x - y + z)^2\)? (a) 2 (b) 4 (c) 6 (d) None of the above

6. 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

7. If each edge of a cube is increased by 10%, by what percentage will its total surface area increase? (a) 10% (b) 20% (c) 21% (d) 23%

8. To dig a pond that is 40 meters long and 30 meters wide, a total cost of ₹51,000 was incurred at the rate of ₹8.50 per cubic meter. What is the depth of the pond? (a) 5 meters (b) 7 meters (c) 11 meters (d) 22 meters

9. From a tank measuring 2.5 meters by 2.2 meters, removing 110 buckets of water causes the water level to drop by 4 decimeters. How much water does each bucket hold in liters? (a) 10 liters (b) 15 liters (c) 20 liters (d) 25 liters

10. If the length of a cuboid is increased by 10%, the width by 20%, and the height is decreased by 30%, what is the percentage change in its volume? (a) 6.5 increased (b) 7.6 increased (c) 6.5decreased (d) 7.6 decreased

11. If a tin container is cube-shaped with each edge measuring 30 cm, what is the maximum amount of water it can hold in liters? (a) 27 liters (b) 24 liters (c) 22 liters (d)

12. 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

13. 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

14. 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

15. 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

16. If the length of the diagonal of a cube is \(8\sqrt{3}\) cm, then what is the length of its edge? (a) 8 cm (b) 4 cm (c) 5 cm (d) 7 cm

17. How many cubes with 10 cm edges can be placed inside a cube-shaped box with 1 meter edge length? (a) 10 (b) 100 (c) 1000 (d) 10000

18. If a hemispherical basin with a diameter of 150 cm can hold 120 times more water than a cone with a height of 15 cm, then what is the diameter of that cone? (a) 27 cm (b) 24 cm (c) 25 cm (d) 26 cm

19. If a right rectangular prism has \(x\) vertices, \(y\) edges, and \(z\) faces, then the value of \((x - y + z)\) is \(8 - 12 + 6 = 2\). (a) 3 (b) 0 (c) 2 (d) 4

20. 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%

21. If three metallic cubes with edges measuring 3 cm, 4 cm, and 5 cm are melted and recast into a new cube, the length of the edge of the new cube will be – (a) 6 cm (b) 7 cm (c) 8 cm (d) 9 cm

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 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

24. 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

25. 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

26. 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

27. The length, width, and height of a room are 5 m, 4 m, and 3 m respectively. What is the maximum length of a rod that can be placed inside the room? (a) \(5\sqrt2\) meters (b) \(7\) meters (c) \(8\sqrt2\) meters (d) \(10\sqrt2\) meters

28. The cube whose total edge length is 60 cm has a volume of — (a) 110 cubic cm (b) 120cubic cm (c) 125 cubic cm (d) 130 cubics

29. If a cube has a side length of \(a\) units and a diagonal length of \(d\) units, then the relationship between \(a\) and \(d\) is—? (a) \(\sqrt2a=d\) (b) \(\sqrt3a=d\) (c) \(a=\sqrt3d\) (d) \(a=\sqrt2d\)

30. If two cubes with a side length of \(2\sqrt6\) cm are placed side by side, then the length of the diagonal of the resulting cuboid will be—? (a) 10 cm (b) 6 cm (c) 2 cm (d) 12 cm

31. In a right-angled quadrilateral, if the number of vertices is denoted by \(x\), the number of sides by \(y\), and the number of diagonals by \(z\), then what is the value of \(x + 3y - 5z\)? (a) 14 (b) 44 (c) 20 (d) 24

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

33. The areas of the three adjacent faces of a right rectangular prism are \(a\), \(b\), and \(c\) square units. Find the length of the space diagonal (the longest diagonal) of the prism.

34. If a right rectangular prism (cuboid) has \(x\) vertices, \(y\) edges, and \(z\) faces, then what is the value of \((x - y + z)\)?

35. If a cube-shaped tin container has each edge measuring 30 cm, what is the maximum amount of water it can hold in liters?

36. The sum of the edges of a cube is 60 cm. What is the volume of the cube?

37. A low-lying plot of land measuring 48 meters in length and 31.5 meters in width is to be raised by 6.5 decimeters. To achieve this, a nearby pit measuring 27 meters in length and 18.2 meters in width is dug. What will be the depth of the pit?

38. 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?

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

40. If a cuboid has \(x\) edges and \(y\) faces, what is the minimum value of \(a\) such that \((x + y + a)\) becomes a perfect square?

41. The space diagonal of a cube is 4√3 cm. Find the total surface area of the cube.

42. 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?

43. Translate the following: "The internal length, width, and height of a tea box are 7.5 decimeters, 6 decimeters, and 5.4 decimeters respectively. The weight of the box when filled with tea is 52 kilograms 350 grams. But when empty, the box weighs 3.75 kilograms. Determine the weight of tea per cubic decimeter."

44. If the length, width, and height of a right rectangular prism are equal, then the special name for that solid object is _____.

45. The length, width, and height of a cuboidal room are respectively \(a\), \(b\), and \(c\) units, and given that \(a + b + c = 25\) and \(ab + bc + ca = 240.5\), what is the length of the longest rod that can be placed inside the room?

46. 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.

47. 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 \(Sd = 6\sqrt{3}V\).

48. From a cube-shaped water tank, 64 buckets of equal size are removed, leaving the tank one-third full. If the side length of the tank is 1.2 meters, then how much water does each bucket hold in liters? (Assume: 1 cubic decimeter = 1 liter)

49. A low-lying plot of land measuring 48 meters in length and 31.5 meters in width has been raised by 6.5 decimeters. To achieve this, soil will be excavated from an adjacent plot measuring 27 meters in length and 18.2 meters in width. Determine the depth of the excavation in meters.

50. 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."

51. 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.

52. If a cuboid has number of faces = x, number of edges = y, number of vertices = z, and number of diagonals = p, then what is the value of (x − y + z + p)?

53. A rectangular tank measuring 2.1 meters in length and 1.5 meters in width is half-filled with water. If 630 liters of water is poured into the tank, determine how much the water level will rise.

54. If the length of the diagonal of a cube is \(5\sqrt{3}\) cm, find its volume.

55. A wooden log measuring 4 meters in length, 5 decimeters in width, and 3 decimeters in thickness was used to cut 40 planks, each 2 meters long and 2 decimeters wide. 2% of the wood was wasted during cutting, and 108 cubic decimeters of wood still remain in the log. Determine the thickness of each plank.

56. If the length of the diagonal of each face of a cube is \(6\sqrt{2}\) cm, what is the total surface area of the cube?