hemispheres, rectangular parallelepiped, regular right pyramid with triangular or square base - One Line Questions

1. What is the ratio of the volume of a sphere to the volume of a hemisphere with the same radius? — 2:1
2. Calculate the total surface area of a rectangular parallelepiped with length 10 cm, width 5 cm, and height 2 cm. — 140 sq cm
3. What is the total surface area of a regular pyramid with a square base of side 10 cm and a slant height of 12 cm? — 220 sq cm
4. If a rectangular parallelepiped has dimensions 5 cm, 4 cm, and 3 cm, what is its volume? — 60 cubic cm
5. If the area of the base of a rectangular parallelepiped is 20 sq cm and its height is 6 cm, what is its volume? — 120 cubic cm
6. Calculate the volume of a regular right pyramid with a triangular base of area 15 sq cm and a height of 8 cm. — 40 cubic cm
7. A regular pyramid has a square base of side 5 cm and a slant height of 13 cm. What is its lateral surface area? — 260 sq cm
8. If the radius of a hemisphere is 7 cm, what is its volume? (Use pi = 22/7) — 718.67 cubic cm
9. A regular right pyramid has a square base of side 6 cm. If its height is 4 cm, what is its volume? — 48 cubic cm
10. What is the lateral surface area of a rectangular parallelepiped if the perimeter of the base is 20 cm and its height is 8 cm? — 160 sq cm
11. The lateral surface area of a regular pyramid with a triangular base of perimeter 18 cm and slant height 10 cm is: — 90 sq cm
12. A regular pyramid has a square base. If the side length of the base is doubled, by what factor does the volume increase, assuming the height remains constant? — 4
13. What is the total surface area of a hemisphere with radius 'r'? — 3 * pi * r^2
14. A cuboid has a volume of 120 cubic cm. If its length is 6 cm and width is 5 cm, what is its height? — 4 cm
15. If the area of the base of a regular pyramid is 25 sq cm and its volume is 75 cubic cm, what is its height? — 9 cm
16. If the slant height of a regular pyramid with a square base is 5 cm and the height is 4 cm, what is the length of the side of the base? — 3 cm
17. A solid hemisphere has a total surface area of 192.5 sq cm. Find its radius. — 3.5 cm
18. The base of a regular pyramid is an equilateral triangle with side 6 cm. If the height is 10 cm, what is its volume? — 30 * sqrt(3) cubic cm
19. Calculate the curved surface area of a hemisphere with a diameter of 14 cm. — 308 sq cm
20. What is the volume of a hemisphere whose radius is 3 units? — 18 * pi cubic units
21. The curved surface area of a hemisphere is given by which formula, where 'r' is the radius? — 2 * pi * r^2
22. A regular pyramid has a square base with side 12 cm. If its volume is 576 cubic cm, find its height. — 8 cm
23. If the total surface area of a hemisphere is 48 * pi sq units, what is its radius? — 6 units
24. What is the formula for the volume of a hemisphere with radius 'r'? — 2/3 * pi * r^3
25. A hemispherical bowl has an inner radius of 10 cm. What is its capacity (volume)? — 2093.33 cubic cm
26. A hemisphere has a radius of 10 cm. What is its volume? — 2094.40 cubic cm
27. What is the slant height of a regular pyramid with a square base of side 8 cm and a height of 3 cm? — 10 cm
28. If the total surface area of a rectangular parallelepiped is 220 sq cm and its length and width are 10 cm and 5 cm respectively, find its height. — 5 cm
29. If the diameter of a hemisphere is 20 cm, what is its total surface area? — 942.86 sq cm
30. What is the volume of a hemisphere with a diameter of 6 cm? — 18 * pi cubic cm
31. If a rectangular parallelepiped has its length, width, and height in the ratio 3:2:1 and its volume is 162 cubic cm, find its dimensions. — 6 cm, 4 cm, 3 cm
32. A regular pyramid has a square base of side length 4 cm and a height of 6 cm. What is its volume? — 32 cubic cm
33. What is the formula for the volume of a pyramid with base area 'A' and height 'h'? — 1/3 * A * h
34. What is the shape of the cross-section when a hemisphere is cut by a plane parallel to its base? — A circle
35. What is the shape of the base of a regular right pyramid? — A regular polygon
36. In a regular right pyramid, the height is the perpendicular distance from the apex to: — The centroid of the base
37. The total surface area of a closed hemisphere is equal to the sum of its curved surface area and: — Area of the base
38. What is the total surface area of a regular pyramid? — Base Area + Lateral Surface Area
39. What is a rectangular parallelepiped also known as? — Cuboid
40. The total surface area of a rectangular parallelepiped is given by which formula? — 2(lw + wh + hl)
41. What is the formula for the volume of a rectangular parallelepiped with length 'l', width 'w', and height 'h'? — l * w * h
42. A cube is a special case of a rectangular parallelepiped where: — Length = Width = Height
43. What are the dimensions of a rectangular parallelepiped? — Length, Width, Height
44. The sum of the lengths of all edges of a rectangular parallelepiped with dimensions l, w, h is: — 4(l + w + h)
45. What is the lateral surface area of a regular pyramid with perimeter of the base 'P' and slant height 'l'? — 1/2 * P * l
46. What is the relationship between the volume of a pyramid and a prism with the same base area and height? — Pyramid volume is one-third the prism volume
47. The surface area of a hemisphere is increased by 100%. By what factor does the radius increase? — sqrt(2)
48. A rectangular parallelepiped has edges of length 3 cm, 4 cm, and 5 cm. What is the length of its longest diagonal? — sqrt(75) cm
49. What is the length of the diagonal of a rectangular parallelepiped with dimensions l, w, and h? — sqrt(l^2 + w^2 + h^2)
50. In a regular right pyramid, the apex is directly above the centroid of which part? — The base
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