Mensuration of Plane and Solid Figures - Question Bank
1. A parallelogram has sides of length 10 cm and 8 cm. If the angle between them is 30°, what is its area?
2. The ratio of the radii of two circles is 2:3 and the ratio of their areas is:
3. What is the surface area of a sphere whose volume is 288π cubic cm?
4. A rectangular garden is 40 m long and 30 m wide. A path 2 m wide is built around it. What is the area of the path?
5. What is the volume of a right circular cylinder whose radius is 7 cm and height is 10 cm? (Use π = 22/7)
6. If the radius of a circle is increased by 50%, by what percentage does its area increase?
7. The lengths of the diagonals of a rhombus are 12 cm and 16 cm. What is its area?
8. What is the area of the largest circle that can be inscribed in a square of side 14 cm?
9. A solid metallic sphere of radius 10 cm is melted and recast into small cones of radius 2 cm and height 5 cm. How many such cones can be formed?
10. The perimeter of a rhombus is 52 cm and one diagonal is 24 cm. What is the length of the other diagonal?
11. What is the total surface area of a hemisphere with radius 6 cm? (Use π = 22/7)
12. If a rectangle's length is increased by 10% and its width is decreased by 10%, what is the net percentage change in its area?
13. What is the area of the region between two concentric circles with radii 7 cm and 14 cm? (Use π = 22/7)
14. The sum of the radii of two circles is 10 cm and the difference of their circumferences is 8π cm. What is the radius of the larger circle?
15. A rectangular plot is 100 m long and 80 m wide. What is the cost of gravelling it at Rs 5 per sq meter?
16. What is the volume of a cone with radius 3 cm and height 7 cm? (Use π = 22/7)
17. If the area of a rhombus is 24 sq cm and its perimeter is 20 cm, what is the length of its altitude?
18. What is the lateral surface area of a cube with side length 4 cm?
19. The area of a parallelogram is 120 sq cm and its height is 10 cm. What is its base length?
20. A circular garden has a radius of 14 meters. What is its area? (Use π = 22/7)
21. What is the volume of a cube whose total surface area is 216 sq cm?
22. The perimeter of a square is 36 cm. What is its diagonal length?
23. The slant height of a cone is 13 cm and its radius is 5 cm. What is its height?
24. What is the sum of the areas of two circles with radii 3 cm and 4 cm? (Use π = 22/7)
25. A rectangle's length is twice its width. If its area is 72 sq cm, what is its length?
26. What is the total surface area of a cylinder with radius 5 cm and height 10 cm? (Use π = 22/7)
27. The sides of a triangle are 3 cm, 4 cm, and 5 cm. What is its area?
28. What is the volume of a hemisphere with a diameter of 12 cm?
29. The circumference of a circle is 44 cm. What is its area? (Use π = 22/7)
30. A square is inscribed in a circle of radius 7 cm. What is the area of the square?
31. If the area of a circle is 100π sq cm, what is its diameter?
32. What is the volume of a pyramid with a square base of side 6 cm and a height of 10 cm?
33. The perimeter of a regular hexagon with side length 'a' is:
34. What is the area of a sector of a circle with radius 6 cm and angle 60°? (Use π = 22/7)
35. The dimensions of a cuboid are 10 cm, 5 cm, and 4 cm. What is its total surface area?
36. If the area of a rhombus is 150 sq cm and one of its diagonals is 15 cm, what is the length of the other diagonal?
37. What is the lateral surface area of a cone with radius 3 cm and slant height 5 cm?
38. The lengths of the parallel sides of a trapezoid are 12 cm and 18 cm, and its height is 7 cm. What is its area?
39. What is the volume of a cylinder with a radius of 7 cm and a height of 10 cm? (Use π = 22/7)
40. The surface area of a sphere is 144π sq cm. What is its radius?
41. A parallelogram has a base of 15 cm and a height of 8 cm. What is its area?
42. The diagonal of a square is 10√2 cm. What is the length of its side?
43. If the radius of a hemisphere is 3 cm, what is its volume?
44. What is the area of a triangle with a base of 10 cm and a height of 6 cm?
45. The diameter of a circle is 28 cm. What is its circumference?
46. A rectangular field is 50 meters long and 30 meters wide. What is its perimeter?
47. What is the volume of a cube with a side length of 5 cm?
48. The area of a circle is 154 sq cm. What is its radius?
49. If the length of a rectangle is 12 cm and its breadth is 8 cm, what is its area?
50. The perimeter of a square is 48 cm. What is its area?