Mensuration - Question Bank

1. If the area of an equilateral triangle is √3/4 * a^2, what is the area of an equilateral triangle with a side length of 2 cm?
A) √3 sq cm
B) 2√3 sq cm
C) 4√3 sq cm
D) 3√3 sq cm
2. What is the ratio of the volume of a sphere to the volume of a cylinder that perfectly encloses it (same radius and height)?
A) 1:1
B) 2:3
C) 3:2
D) 1:2
3. The lengths of the parallel sides of a trapezoid are 7 cm and 10 cm, and its area is 51 sq cm. What is its height?
A) 3 cm
B) 6 cm
C) 51 cm
D) 17 cm
4. What is the perimeter of a regular hexagon with side length 8 cm?
A) 48 cm
B) 64 cm
C) 14 cm
D) 24 cm
5. A sector of a circle has a radius of 10 cm and an angle of 90 degrees. What is its area?
A) 10 pi sq cm
B) 25 pi sq cm
C) 50 pi sq cm
D) 100 pi sq cm
6. What is the volume of a pyramid with a square base of side 4 cm and a height of 6 cm?
A) 32 cubic cm
B) 16 cubic cm
C) 96 cubic cm
D) 48 cubic cm
7. Find the area of a trapezoid with parallel sides of length 8 cm and 12 cm, and a height of 5 cm.
A) 20 sq cm
B) 50 sq cm
C) 100 sq cm
D) 40 sq cm
8. The diameter of a circle is 20 cm. What is its radius?
A) 5 cm
B) 10 cm
C) 20 cm
D) 40 cm
9. What is the surface area of a cube with side length 5 cm?
A) 75 sq cm
B) 125 sq cm
C) 150 sq cm
D) 30 sq cm
10. A cylindrical can has a radius of 7 cm and a height of 10 cm. What is its volume (use pi = 22/7)?
A) 1540 cubic cm
B) 440 cubic cm
C) 3080 cubic cm
D) 220 cubic cm
11. What is the volume of a rectangular prism with length 8 cm, width 3 cm, and height 4 cm?
A) 15 cubic cm
B) 96 cubic cm
C) 12 cubic cm
D) 32 cubic cm
12. The area of a parallelogram is 30 sq cm and its base is 6 cm. What is its height?
A) 5 cm
B) 180 cm
C) 10 cm
D) 36 cm
13. What is the perimeter of a rhombus with side length 6 cm?
A) 12 cm
B) 24 cm
C) 36 cm
D) 6 cm
14. The area of a rhombus is 50 sq cm and one of its diagonals is 10 cm. What is the length of the other diagonal?
A) 5 cm
B) 20 cm
C) 10 cm
D) 25 cm
15. If the diagonal of a square is 10√2 cm, what is its side length?
A) 10 cm
B) 20 cm
C) 5 cm
D) 100 cm
16. Find the total surface area of a hemisphere with radius 4 cm.
A) 32 pi sq cm
B) 48 pi sq cm
C) 80 pi sq cm
D) 16 pi sq cm
17. Calculate the curved surface area of a hemisphere with radius 5 cm.
A) 50 pi sq cm
B) 75 pi sq cm
C) 100 pi sq cm
D) 25 pi sq cm
18. What is the volume of a hemisphere with radius 6 cm?
A) 144 cubic cm
B) 288 cubic cm
C) 452.4 cubic cm
D) 904.8 cubic cm
19. Find the surface area of a sphere with radius 7 cm (use pi = 22/7).
A) 154 sq cm
B) 616 sq cm
C) 44 sq cm
D) 88 sq cm
20. What is the volume of a sphere with radius 3 cm?
A) 36 cubic cm
B) 108 cubic cm
C) 113.1 cubic cm
D) 28.3 cubic cm
21. Calculate the total surface area of a cone with radius 3 cm and slant height 5 cm.
A) 15 sq cm
B) 24 pi sq cm
C) 75.4 sq cm
D) 47.1 sq cm
22. What is the curved surface area of a cone with radius 5 cm and slant height 13 cm?
A) 65 sq cm
B) 204.2 sq cm
C) 282.7 sq cm
D) 100 sq cm
23. Find the volume of a cone with radius 6 cm and height 10 cm.
A) 60 cubic cm
B) 188.5 cubic cm
C) 377 cubic cm
D) 120 cubic cm
24. What is the total surface area of a cylinder with radius 2 cm and height 5 cm?
A) 40 sq cm
B) 70 sq cm
C) 94.2 sq cm
D) 125.6 sq cm
25. Calculate the lateral surface area of a cylinder with radius 3 cm and height 7 cm.
A) 21 sq cm
B) 42 sq cm
C) 132 sq cm
D) 66 sq cm
26. A cuboid has dimensions 5 cm x 4 cm x 3 cm. What is its volume?
A) 12 cubic cm
B) 47 cubic cm
C) 60 cubic cm
D) 72 cubic cm
27. Find the area of a circle with a diameter of 14 cm (use pi = 22/7).
A) 44 sq cm
B) 616 sq cm
C) 154 sq cm
D) 88 sq cm
28. What is the circumference of a circle with a radius of 7 cm (use pi = 22/7)?
A) 44 cm
B) 154 cm
C) 22 cm
D) 88 cm
29. A triangle has a base of 8 cm and a height of 6 cm. What is its area?
A) 14 sq cm
B) 24 sq cm
C) 48 sq cm
D) 12 sq cm
30. Calculate the volume of a cube with an edge of 3 cm.
A) 9 cubic cm
B) 18 cubic cm
C) 27 cubic cm
D) 81 cubic cm
31. A square has a side of 7 meters. What is its perimeter?
A) 14 meters
B) 49 meters
C) 28 meters
D) 7 meters
32. If the length of a rectangle is 10 cm and its width is 5 cm, what is its area?
A) 15 sq cm
B) 50 sq cm
C) 30 sq cm
D) 100 sq cm
33. What is the total surface area of a hemisphere?
A) 2 * pi * r^2
B) 4 * pi * r^2
C) (2/3) * pi * r^3
D) 3 * pi * r^2
34. The curved surface area of a hemisphere is:
A) 2 * pi * r^2
B) 4 * pi * r^2
C) (2/3) * pi * r^3
D) pi * r^2
35. What is the volume of a hemisphere with radius 'r'?
A) 2 * pi * r^3
B) (2/3) * pi * r^3
C) 4 * pi * r^2
D) (4/3) * pi * r^3
36. The surface area of a sphere with radius 'r' is:
A) (4/3) * pi * r^3
B) 2 * pi * r^2
C) 4 * pi * r^2
D) pi * r^2
37. What is the volume of a sphere with radius 'r'?
A) 4 * pi * r^2
B) (4/3) * pi * r^3
C) pi * r^3
D) 2 * pi * r^2
38. The total surface area of a cone is:
A) pi * r * l
B) pi * r^2 * h
C) pi * r (r + l)
D) 2 * pi * r * h
39. What is the curved surface area of a cone?
A) pi * r * l
B) pi * r^2 * l
C) pi * r (r + l)
D) (1/3) * pi * r^2 * h
40. The volume of a cone with radius 'r' and height 'h' is:
A) pi * r^2 * h
B) (1/3) * pi * r^2 * h
C) 2 * pi * r * h
D) (1/3) * pi * r (r + l)
41. What is the total surface area of a cylinder?
A) 2 * pi * r * h
B) pi * r^2 * h
C) 2 * pi * r (r + h)
D) pi * r (r + h)
42. The curved surface area of a cylinder is:
A) pi * r^2 * h
B) 2 * pi * r * h
C) 2 * pi * r (r + h)
D) 2 * pi * r^2
43. What is the volume of a cylinder with radius 'r' and height 'h'?
A) 2 * pi * r * h
B) pi * r^2
C) pi * r^2 * h
D) 2 * pi * r^2 * h
44. The total surface area of a cuboid is:
A) 2 * (lh + wh)
B) l * w * h
C) 2 * (lw + lh + wh)
D) lw + lh + wh
45. What is the lateral surface area of a cuboid with length 'l', width 'w', and height 'h'?
A) 2 * (lw + lh + wh)
B) l * w * h
C) 2 * (lh + wh)
D) 2 * (lw + lh)
46. The area of a circle with radius 'r' is:
A) 2 * pi * r
B) pi * r
C) pi * r^2
D) 2 * pi * r^2
47. What is the formula for the circumference of a circle?
A) pi * r^2
B) 2 * pi * r
C) pi * d
D) 2 * r
48. The area of a triangle is given by:
A) Base * Height
B) 0.5 * Base * Height
C) 2 * Base * Height
D) 0.5 * (Base + Height)
49. What is the volume of a cube with side length 's'?
A) 6 * s^2
B) s^3
C) 3 * s
D) 12 * s
50. Which formula calculates the perimeter of a square?
A) Side * Side
B) 4 * Side
C) 2 * Side
D) Side / 4
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