mensuration of plane figures, mensuration of solid figures, area and volume calculations - Question Bank

1. What is the ratio of the volume of a sphere to the volume of a cylinder that has the same radius and height equal to the diameter of the sphere?
A) 1:1
B) 1:2
C) 2:3
D) 3:2
2. If the length of a diagonal of a square is 10√2 cm, what is its area?
A) 100 sq cm
B) 200 sq cm
C) 50 sq cm
D) 10√2 sq cm
3. A sector of a circle has radius 10 cm and angle 90 degrees. What is its area (use π = 22/7)?
A) 78.5 sq cm
B) 157 sq cm
C) 785 sq cm
D) 15.7 sq cm
4. What is the surface area of a cuboid with length 8 cm, width 5 cm, and height 3 cm?
A) 40 sq cm
B) 120 sq cm
C) 158 sq cm
D) 240 sq cm
5. A pyramid has a square base of side 6 cm and a height of 10 cm. What is its volume?
A) 60 cubic cm
B) 120 cubic cm
C) 180 cubic cm
D) 360 cubic cm
6. What is the volume of a prism whose base area is 25 sq cm and height is 8 cm?
A) 33 cubic cm
B) 100 cubic cm
C) 200 cubic cm
D) 400 cubic cm
7. A circle is inscribed in a square of side 10 cm. What is the area of the circle (use π = 3.14)?
A) 31.4 sq cm
B) 62.8 sq cm
C) 78.5 sq cm
D) 314 sq cm
8. What is the perimeter of a square whose area is 196 sq meters?
A) 14 meters
B) 56 meters
C) 28 meters
D) 196 meters
9. The base of a triangle is 15 cm and its area is 75 sq cm. What is its height?
A) 5 cm
B) 10 cm
C) 25 cm
D) 30 cm
10. A cylinder has a diameter of 10 cm and a height of 7 cm. What is its volume (use π = 22/7)?
A) 220 cubic cm
B) 550 cubic cm
C) 1100 cubic cm
D) 154 cubic cm
11. What is the total surface area of a hemisphere with radius 'r'?
A) 2πr^2
B) 4πr^2
C) 3πr^2
D) πr^2
12. A sphere has a volume of 4500π cubic cm. What is its radius?
A) 15 cm
B) 30 cm
C) 45 cm
D) 75 cm
13. What is the area of a regular pentagon with side length 'a'?
A) 5a^2
B) 1/4 * sqrt(5(5+2sqrt(5))) * a^2
C) a^2 * sqrt(3)
D) 6a^2
14. A trapezoid has parallel sides of length 8 cm and 12 cm, and its height is 5 cm. What is its area?
A) 20 sq cm
B) 40 sq cm
C) 50 sq cm
D) 100 sq cm
15. If the area of a rhombus is 150 sq cm and one of its diagonals is 20 cm, what is the length of the other diagonal?
A) 7.5 cm
B) 15 cm
C) 30 cm
D) 300 cm
16. A cone has a radius of 9 cm and a height of 12 cm. What is its volume (use π = 3.14)?
A) 1017.36 cubic cm
B) 3052.08 cubic cm
C) 339.12 cubic cm
D) 942 cubic cm
17. What is the curved surface area of a cone with radius 6 cm and slant height 10 cm?
A) 60π sq cm
B) 36π sq cm
C) 96π sq cm
D) 100π sq cm
18. A cylinder has a radius of 7 cm and a height of 15 cm. What is its volume (use π = 22/7)?
A) 2310 cubic cm
B) 6930 cubic cm
C) 462 cubic cm
D) 346.5 cubic cm
19. The surface area of a sphere is 616 sq cm. What is its radius (use π = 22/7)?
A) 7 cm
B) 14 cm
C) 21 cm
D) 49 cm
20. What is the volume of a cuboid with dimensions 4 cm x 5 cm x 6 cm?
A) 15 cubic cm
B) 120 cubic cm
C) 30 cubic cm
D) 24 cubic cm
21. A circle has a circumference of 88 cm. What is its radius (use π = 22/7)?
A) 14 cm
B) 7 cm
C) 28 cm
D) 44 cm
22. What is the perimeter of a triangle with sides 5 cm, 7 cm, and 9 cm?
A) 21 cm
B) 11 cm
C) 35 cm
D) 16 cm
23. A rectangular field is 100 meters long and 50 meters wide. What is its area?
A) 150 sq meters
B) 5000 sq meters
C) 300 meters
D) 250 sq meters
24. If the volume of a cube is 125 cubic cm, what is the length of its edge?
A) 5 cm
B) 25 cm
C) 125 cm
D) approx. 5.01 cm
25. Calculate the total surface area of a cylinder with radius 'r' and height 'h'.
A) 2πrh
B) πr^2h
C) 2πr(r+h)
D) πr(r+h)
26. What is the volume of a hemisphere with radius 'r'?
A) 4/3 πr^3
B) 2/3 πr^3
C) 2πr^2
D) 4πr^2
27. A square has an area of 81 sq meters. What is the length of its side?
A) 9 meters
B) 20.25 meters
C) 81 meters
D) 40.5 meters
28. The perimeter of a rectangle is 40 cm. If the length is 12 cm, what is its width?
A) 8 cm
B) 28 cm
C) 20 cm
D) 6 cm
29. What is the length of the arc of a sector of a circle with radius 'r' and angle 'θ' (in degrees)?
A) (θ/360) * 2πr
B) (θ/180) * πr
C) θ * 2πr
D) (360/θ) * 2πr
30. A sector of a circle has a radius 'r' and angle 'θ' (in degrees). What is the area of the sector?
A) (θ/360) * πr^2
B) (θ/180) * πr
C) θ * πr^2
D) (360/θ) * πr^2
31. If the area of a circle is 154 sq cm, what is its radius (use π = 22/7)?
A) 7 cm
B) 14 cm
C) 49 cm
D) 22 cm
32. What is the total surface area of a cone with radius 'r' and slant height 'l'?
A) πrl
B) 2πr(r+l)
C) πr(r+l)
D) πr^2 + πrl
33. A regular hexagon has a side length 'a'. What is its area?
A) 6a^2
B) 3√3/2 a^2
C) √3/2 a^2
D) 3a^2
34. What is the area of a trapezoid with parallel sides 'a' and 'b' and height 'h'?
A) 1/2 (a+b)h
B) (a+b)h
C) 1/2 ab h
D) ab + h
35. A rhombus has diagonals of length d1 and d2. What is its area?
A) d1 * d2
B) 1/2 (d1 + d2)
C) 1/2 d1 * d2
D) d1 + d2
36. What is the volume of a cone with base radius 'r' and height 'h'?
A) πr^2h
B) 1/3 πr^2h
C) 3πr^2h
D) πrh
37. The slant height of a cone is 'l', and the radius of its base is 'r'. What is the formula for the curved surface area of the cone?
A) πr^2l
B) 2πrl
C) πr(r+l)
D) πrl
38. What is the lateral surface area of a cylinder with radius 'r' and height 'h'?
A) πr^2h
B) 2πrh
C) 2πr(r+h)
D) πrh
39. A cylinder has a radius of 5 cm and a height of 10 cm. What is its volume (use π = 22/7)?
A) 1570 cubic cm
B) 785 cubic cm
C) 157.1 cubic cm
D) 785.7 cubic cm
40. What is the formula for the surface area of a sphere with radius 'r'?
A) 4/3 πr^3
B) πr^2
C) 4πr^2
D) 2πr
41. The radius of a sphere is 3 cm. What is its volume (use π = 3.14)?
A) 28.26 cubic cm
B) 113.04 cubic cm
C) 36 cubic cm
D) 113.1 cubic cm
42. Calculate the volume of a cuboid with length 'l', width 'w', and height 'h'.
A) lw + wh + hl
B) 2(lw + wh + hl)
C) lwh
D) l + w + h
43. What is the volume of a cube with side length 'a'?
A) 6a^2
B) a^2
C) 3a
D) a^3
44. A parallelogram has a base of 12 cm and a height of 5 cm. What is its area?
A) 17 sq cm
B) 60 sq cm
C) 30 sq cm
D) 24 sq cm
45. What is the formula for the area of a circle with radius 'r'?
A) 2πr
B) πr^2
C) 2πr^2
D) 4πr
46. If the diameter of a circle is 14 cm, what is its radius?
A) 7 cm
B) 28 cm
C) 3.5 cm
D) 14 cm
47. What is the circumference of a circle with radius 'r'?
A) πr^2
B) 2πr
C) πr
D) 2πr^2
48. The area of a triangle is given by 1/2 * base * height. If a triangle has a base of 10 cm and a height of 8 cm, what is its area?
A) 18 sq cm
B) 40 sq cm
C) 80 sq cm
D) 16 sq cm
49. Calculate the perimeter of a square with side length 's'.
A) s^2
B) 4s
C) 2s
D) s/4
50. What is the formula for the area of a rectangle with length 'l' and width 'w'?
A) l + w
B) 2(l + w)
C) l * w
D) l / w
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