hemispheres, rectangular parallelepiped, regular right pyramid with triangular or square base - Question Bank

1. A rectangular parallelepiped has edges of length 3 cm, 4 cm, and 5 cm. What is the length of its longest diagonal?
A) sqrt(50) cm
B) sqrt(75) cm
C) sqrt(125) cm
D) sqrt(100) cm
2. If the total surface area of a hemisphere is 48 * pi sq units, what is its radius?
A) 4 units
B) 6 units
C) 8 units
D) 12 units
3. What is the volume of a hemisphere with a diameter of 6 cm?
A) 9 * pi cubic cm
B) 36 * pi cubic cm
C) 18 * pi cubic cm
D) 27 * pi cubic cm
4. The lateral surface area of a regular pyramid with a triangular base of perimeter 18 cm and slant height 10 cm is:
A) 180 sq cm
B) 90 sq cm
C) 270 sq cm
D) 60 sq cm
5. A regular pyramid has a square base with side 12 cm. If its volume is 576 cubic cm, find its height.
A) 4 cm
B) 8 cm
C) 12 cm
D) 16 cm
6. What is the relationship between the volume of a pyramid and a prism with the same base area and height?
A) Pyramid volume is half the prism volume
B) Pyramid volume is one-third the prism volume
C) Pyramid volume is equal to the prism volume
D) Pyramid volume is double the prism volume
7. In a regular right pyramid, the height is the perpendicular distance from the apex to:
A) Any vertex of the base
B) The midpoint of any base edge
C) The center of the base
D) The centroid of the base
8. 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.
A) 5 cm
B) 4 cm
C) 3 cm
D) 2 cm
9. A cube is a special case of a rectangular parallelepiped where:
A) Length = 2 * Width
B) Length = Width = Height
C) Length = Height
D) Width = 2 * Height
10. The surface area of a hemisphere is increased by 100%. By what factor does the radius increase?
A) sqrt(2)
B) 2
C) sqrt(3)
D) 3
11. What is the shape of the cross-section when a hemisphere is cut by a plane parallel to its base?
A) A semicircle
B) A circle
C) An ellipse
D) A point
12. 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?
A) 3 cm
B) 6 cm
C) 4 cm
D) 5 cm
13. 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?
A) 2
B) 4
C) 8
D) 16
14. 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?
A) 160 sq cm
B) 100 sq cm
C) 200 sq cm
D) 80 sq cm
15. 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.
A) 9 cm, 6 cm, 2 cm
B) 6 cm, 4 cm, 3 cm
C) 3 cm, 2 cm, 1 cm
D) 9 cm, 4 cm, 1 cm
16. The total surface area of a closed hemisphere is equal to the sum of its curved surface area and:
A) Area of a great circle
B) Area of a small circle
C) Area of the base
D) Area of the diameter
17. A hemisphere has a radius of 10 cm. What is its volume?
A) 4188.79 cubic cm
B) 2094.40 cubic cm
C) 1256.64 cubic cm
D) 418.88 cubic cm
18. 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?
A) 100 sq cm
B) 120 sq cm
C) 220 sq cm
D) 340 sq cm
19. The base of a regular pyramid is an equilateral triangle with side 6 cm. If the height is 10 cm, what is its volume?
A) 30 * sqrt(3) cubic cm
B) 90 * sqrt(3) cubic cm
C) 10 * sqrt(3) cubic cm
D) 60 * sqrt(3) cubic cm
20. What is the slant height of a regular pyramid with a square base of side 8 cm and a height of 3 cm?
A) 5 cm
B) 10 cm
C) 4 cm
D) 12 cm
21. A regular right pyramid has a square base of side 6 cm. If its height is 4 cm, what is its volume?
A) 16 cubic cm
B) 36 cubic cm
C) 48 cubic cm
D) 96 cubic cm
22. 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?
A) 3 cm
B) 9 cm
C) 25 cm
D) 75 cm
23. What is the total surface area of a regular pyramid?
A) Base Area + Lateral Surface Area
B) Lateral Surface Area only
C) 2 * Base Area + Lateral Surface Area
D) Base Area * Lateral Surface Area
24. A regular pyramid has a square base of side 5 cm and a slant height of 13 cm. What is its lateral surface area?
A) 130 sq cm
B) 260 sq cm
C) 65 sq cm
D) 520 sq cm
25. Calculate the volume of a regular right pyramid with a triangular base of area 15 sq cm and a height of 8 cm.
A) 120 cubic cm
B) 40 cubic cm
C) 60 cubic cm
D) 20 cubic cm
26. A regular pyramid has a square base of side length 4 cm and a height of 6 cm. What is its volume?
A) 96 cubic cm
B) 32 cubic cm
C) 16 cubic cm
D) 48 cubic cm
27. What is the lateral surface area of a regular pyramid with perimeter of the base 'P' and slant height 'l'?
A) P * l
B) 1/2 * P * l
C) 2 * P * l
D) 1/3 * P * l
28. What is the formula for the volume of a pyramid with base area 'A' and height 'h'?
A) A * h
B) 1/3 * A * h
C) 2/3 * A * h
D) 1/2 * A * h
29. In a regular right pyramid, the apex is directly above the centroid of which part?
A) The slant height
B) The lateral faces
C) The base
D) The edges
30. What is the shape of the base of a regular right pyramid?
A) Any polygon
B) A circle
C) A regular polygon
D) An irregular polygon
31. If the area of the base of a rectangular parallelepiped is 20 sq cm and its height is 6 cm, what is its volume?
A) 120 cubic cm
B) 80 cubic cm
C) 26 cubic cm
D) 100 cubic cm
32. The sum of the lengths of all edges of a rectangular parallelepiped with dimensions l, w, h is:
A) lw + wh + hl
B) 2(l + w + h)
C) 4(l + w + h)
D) l + w + h
33. A cuboid has a volume of 120 cubic cm. If its length is 6 cm and width is 5 cm, what is its height?
A) 2 cm
B) 4 cm
C) 3 cm
D) 10 cm
34. What is the length of the diagonal of a rectangular parallelepiped with dimensions l, w, and h?
A) sqrt(l^2 + w^2)
B) sqrt(l^2 + w^2 + h^2)
C) l + w + h
D) sqrt(l^2 + h^2)
35. Calculate the total surface area of a rectangular parallelepiped with length 10 cm, width 5 cm, and height 2 cm.
A) 100 sq cm
B) 160 sq cm
C) 70 sq cm
D) 140 sq cm
36. If a rectangular parallelepiped has dimensions 5 cm, 4 cm, and 3 cm, what is its volume?
A) 12 cubic cm
B) 47 cubic cm
C) 60 cubic cm
D) 20 cubic cm
37. The total surface area of a rectangular parallelepiped is given by which formula?
A) l * w * h
B) l + w + h
C) 2(lw + wh + hl)
D) lw + wh + hl
38. What is the formula for the volume of a rectangular parallelepiped with length 'l', width 'w', and height 'h'?
A) l + w + h
B) 2(lw + wh + hl)
C) l * w * h
D) lw + wh + hl
39. What are the dimensions of a rectangular parallelepiped?
A) Length, Width, Height
B) Radius, Diameter
C) Base, Height
D) Side, Diagonal
40. What is a rectangular parallelepiped also known as?
A) Cube
B) Cylinder
C) Cuboid
D) Cone
41. What is the ratio of the volume of a sphere to the volume of a hemisphere with the same radius?
A) 1:2
B) 2:1
C) 3:2
D) 2:3
42. A hemispherical bowl has an inner radius of 10 cm. What is its capacity (volume)?
A) 4186.67 cubic cm
B) 2093.33 cubic cm
C) 1256 cubic cm
D) 418.67 cubic cm
43. If the diameter of a hemisphere is 20 cm, what is its total surface area?
A) 628.57 sq cm
B) 1257.14 sq cm
C) 942.86 sq cm
D) 314.29 sq cm
44. What is the volume of a hemisphere whose radius is 3 units?
A) 36 * pi cubic units
B) 18 * pi cubic units
C) 27 * pi cubic units
D) 9 * pi cubic units
45. A solid hemisphere has a total surface area of 192.5 sq cm. Find its radius.
A) 3.5 cm
B) 7 cm
C) 5 cm
D) 10 cm
46. Calculate the curved surface area of a hemisphere with a diameter of 14 cm.
A) 308 sq cm
B) 616 sq cm
C) 154 sq cm
D) 462 sq cm
47. If the radius of a hemisphere is 7 cm, what is its volume? (Use pi = 22/7)
A) 1437.33 cubic cm
B) 718.67 cubic cm
C) 2156 cubic cm
D) 1437 cm
48. What is the total surface area of a hemisphere with radius 'r'?
A) 2 * pi * r^2
B) 4 * pi * r^2
C) 3 * pi * r^2
D) pi * r^2
49. The curved surface area of a hemisphere is given by which formula, where 'r' is the radius?
A) 4 * pi * r^2
B) 2 * pi * r^2
C) pi * r^2
D) 3 * pi * r^2
50. What is the formula for the volume of a hemisphere with radius 'r'?
A) 4/3 * pi * r^3
B) 2/3 * pi * r^3
C) pi * r^2 * h
D) 1/3 * pi * r^2 * h
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