right prism, right circular cone, right circular cylinder, sphere - Question Bank

1. A right circular cone is inscribed in a sphere of radius R. If the height of the cone is h, what is its volume?
A) (1/3)πh²(2R-h)
B) (1/3)πh²(R-h)
C) (1/3)πh²(2R+h)
D) (1/3)πh(R²-h²)
2. What is the volume of a right circular cylinder with radius 8 cm and height 3 cm?
A) 24π cm³
B) 48π cm³
C) 192π cm³
D) 768π cm³
3. A right prism has a base that is an isosceles triangle with sides 5 cm, 5 cm, and 6 cm. If the height of the prism is 10 cm, what is its volume?
A) 150 cm³
B) 120 cm³
C) 60 cm³
D) 30 cm³
4. The volume of a sphere is 36π cm³. What is its surface area?
A) 12π cm²
B) 36π cm²
C) 108π cm²
D) 144π cm²
5. A right circular cone has a base area of 36π cm². If its height is 10 cm, what is its volume?
A) 120π cm³
B) 180π cm³
C) 360π cm³
D) 1080π cm³
6. What is the ratio of the volume of a sphere to the volume of a right circular cylinder that circumscribes it (same radius and height equal to diameter)?
A) 1:1
B) 2:3
C) 3:2
D) 1:2
7. The lateral surface area of a right circular cylinder is 110 cm² and its radius is 5 cm. What is its height?
A) 3.5 cm
B) 7 cm
C) 11 cm
D) 22 cm
8. A right prism has a rectangular base of 4 cm by 6 cm and a height of 10 cm. What is its total surface area?
A) 120 cm²
B) 168 cm²
C) 208 cm²
D) 248 cm²
9. What is the total surface area of a right circular cone with radius 3 cm and slant height 5 cm?
A) 15π cm²
B) 24π cm²
C) 30π cm²
D) 45π cm²
10. If the diameter of a sphere is 12 cm, what is its volume?
A) 72π cm³
B) 144π cm³
C) 288π cm³
D) 432π cm³
11. What is the volume of a right circular cone with slant height 13 cm and base radius 5 cm?
A) 100π cm³
B) 120π cm³
C) 150π cm³
D) 180π cm³
12. The volume of a right circular cylinder is 540π cm³ and its height is 15 cm. What is its radius?
A) 3 cm
B) 6 cm
C) 9 cm
D) 18 cm
13. A right prism has a hexagonal base with side length 4 cm and a height of 6 cm. If the area of the hexagonal base is approximately 41.57 cm², what is its volume?
A) 249.42 cm³
B) 166.28 cm³
C) 83.14 cm³
D) 24.94 cm³
14. What is the surface area of a sphere with radius 7 cm?
A) 49π cm²
B) 98π cm²
C) 196π cm²
D) 294π cm²
15. A right circular cone has a base radius of 8 cm and a height of 15 cm. What is its slant height?
A) 15 cm
B) 17 cm
C) 20 cm
D) 23 cm
16. What is the lateral surface area of a right prism whose base is a square of side 5 cm and height is 8 cm?
A) 40 cm²
B) 80 cm²
C) 160 cm²
D) 200 cm²
17. If the radius of a sphere is tripled, its volume will be multiplied by what factor?
A) 3
B) 6
C) 9
D) 27
18. What is the volume of a right circular cylinder with radius 10 cm and height 5 cm?
A) 50π cm³
B) 100π cm³
C) 250π cm³
D) 500π cm³
19. The base of a right prism is a rhombus with diagonals 8 cm and 6 cm. If the height of the prism is 10 cm, what is its volume?
A) 240 cm³
B) 120 cm³
C) 48 cm³
D) 24 cm³
20. A right circular cone has a slant height of 10 cm and a base radius of 6 cm. What is its height?
A) 6 cm
B) 8 cm
C) 10 cm
D) 12 cm
21. What is the volume of a sphere with radius 3 cm?
A) 9π cm³
B) 27π cm³
C) 36π cm³
D) 108π cm³
22. A right prism has a square base of side 6 cm and a height of 10 cm. What is its lateral surface area?
A) 60 cm²
B) 120 cm²
C) 240 cm²
D) 360 cm²
23. A right circular cylinder has a radius of 3 cm and a height of 5 cm. What is its lateral surface area?
A) 15π cm²
B) 30π cm²
C) 45π cm²
D) 60π cm²
24. What is the formula for the total surface area of a right circular cone?
A) πrl
B) 2πrl
C) πr(r+l)
D) 2πr(r+l)
25. The surface area of a sphere is 144π cm². What is its radius?
A) 4 cm
B) 6 cm
C) 12 cm
D) 36 cm
26. A right prism has a base that is a regular pentagon with side length 3 cm and a height of 7 cm. If the apothem of the pentagon is approximately 2.06 cm, what is its volume?
A) 21.63 cm³
B) 72.1 cm³
C) 10.3 cm³
D) 144.2 cm³
27. What is the volume of a right circular cone with radius 6 cm and height 10 cm?
A) 60π cm³
B) 120π cm³
C) 180π cm³
D) 200π cm³
28. A right circular cylinder has a diameter of 12 cm and a height of 7 cm. What is its total surface area?
A) 252π cm²
B) 132π cm²
C) 360π cm²
D) 144π cm²
29. The radius of a sphere is 9 cm. What is its volume?
A) 972π cm³
B) 243π cm³
C) 729π cm³
D) 324π cm³
30. A right prism has a triangular base with sides 3 cm, 4 cm, and 5 cm. If the height of the prism is 10 cm, what is its volume?
A) 60 cm³
B) 30 cm³
C) 15 cm³
D) 150 cm³
31. What is the lateral surface area of a right circular cone with radius 'r' and slant height 'l'?
A) πrl
B) 2πrl
C) πr(r+l)
D) 2πr(r+l)
32. If the radius of a sphere is decreased by half, its surface area will be multiplied by what factor?
A) 1/2
B) 1/4
C) 1/8
D) 1/16
33. A right circular cone has a volume of 36π cm³ and a base radius of 3 cm. What is its height?
A) 4 cm
B) 9 cm
C) 12 cm
D) 16 cm
34. The radius of the base of a right circular cylinder is 5 cm and its height is 8 cm. What is its volume?
A) 40π cm³
B) 200π cm³
C) 160π cm³
D) 80π cm³
35. What is the surface area of a sphere with a diameter of 10 cm?
A) 100π cm²
B) 200π cm²
C) 400π cm²
D) 50π cm²
36. A right prism has a rectangular base of 5 cm by 7 cm and a height of 12 cm. What is its volume?
A) 420 cm³
B) 140 cm³
C) 84 cm³
D) 210 cm³
37. The total surface area of a right circular cylinder is given by which formula?
A) 2πrh
B) πr²h
C) 2πr(r+h)
D) πr(r+h)
38. A right circular cone has a base radius of 3 cm and a height of 4 cm. What is its slant height?
A) 5 cm
B) 6 cm
C) 7 cm
D) 8 cm
39. What is the formula for the volume of a sphere with radius 'r'?
A) 4πr²
B) 2πr²
C) (4/3)πr³
D) πr²h
40. The base of a right prism is an equilateral triangle with side length 6 cm. If the height of the prism is 9 cm, what is its volume?
A) 81√3 cm³
B) 54√3 cm³
C) 27√3 cm³
D) 162 cm³
41. A right circular cylinder has a radius of 4 cm and a height of 10 cm. What is its lateral surface area?
A) 40π cm²
B) 80π cm²
C) 160π cm²
D) 120π cm²
42. What is the radius of a sphere whose volume is 288π cm³?
A) 3 cm
B) 6 cm
C) 9 cm
D) 12 cm
43. The diameter of the base of a right circular cone is 10 cm and its height is 12 cm. What is its volume?
A) 100π cm³
B) 400π cm³
C) 120π cm³
D) 360π cm³
44. A right prism has a square base with side length 5 cm and a height of 8 cm. What is its total surface area?
A) 180 cm²
B) 200 cm²
C) 240 cm²
D) 160 cm²
45. What is the lateral surface area of a right circular cylinder with radius 'r' and height 'h'?
A) 2πrh
B) πr²h
C) 2πr(r+h)
D) πr(r+h)
46. If the radius of a sphere is doubled, its volume will be multiplied by what factor?
A) 2
B) 4
C) 8
D) 16
47. A right circular cone has a slant height of 13 cm and a base radius of 5 cm. What is its height?
A) 12 cm
B) 8 cm
C) 18 cm
D) 10 cm
48. The radius of the base of a right circular cylinder is 7 cm and its height is 15 cm. What is its volume?
A) 735π cm³
B) 210π cm³
C) 105π cm³
D) 735 cm³
49. What is the surface area of a sphere with radius 'r'?
A) 4πr²
B) 2πr²
C) (4/3)πr³
D) πr²
50. A right prism has a base that is a regular hexagon with side length 4 cm. If the height of the prism is 10 cm, what is its volume?
A) 240√3 cm³
B) 120√3 cm³
C) 24√3 cm³
D) 480 cm³
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