Mensuration

Volume and Surface Area Questions

1. A cylindrical tank has a radius of 21 cm and height of 50 cm. Find its volume and total surface area.
2. A sphere has a diameter of 14 cm. Calculate its surface area and volume.
3. A cone with a base radius of 7 cm and height of 24 cm is cut into two equal parts by a plane parallel to its base. Find the volumes of both parts.
4. A hemisphere has a radius of 10 cm. Find its curved surface area and volume.
5. The dimensions of a cuboid are 12 cm × 8 cm × 6 cm. Calculate its total surface area and volume.
6. A hollow cylinder has an outer radius of 10 cm, an inner radius of 7 cm, and a height of 15 cm. Find its volume.
7. A cube with a side length of 8 cm is painted on all its faces. If it is cut into 1 cm cubes, how many cubes will have exactly two faces painted?
8. A square pyramid has a base side of 10 cm and a height of 15 cm. Calculate its volume.
9. A cylindrical tin is 20 cm tall and has a base radius of 7 cm. Find the cost of painting its outer surface at Rs. 5 per square centimeter.
10. A sphere is inscribed in a cube with a side of 12 cm. Find the volume of the sphere.
11. A bucket is in the shape of a frustum of a cone. The radii of its top and bottom circular ends are 20 cm and 10 cm, respectively, and its height is 30 cm. Find its volume.
12. A cuboid tank is 8 m long, 6 m wide, and 4 m high. It is filled with water to a depth of 3 m. How many liters of water are in the tank?
13. A pipe has an internal diameter of 3 cm. If water flows through the pipe at 10 m/s, find the volume of water delivered in one minute.
14. A cone and a cylinder have the same base radius of 5 cm and the same height of 12 cm. Compare their volumes.
15. A pyramid has a square base of side 9 m and a vertical height of 7 m. Calculate its volume.
16. A hollow spherical shell has an outer radius of 15 cm and an inner radius of 12 cm. Find the volume of the material used.
17. A metal cube with a side length of 6 cm is melted and recast into small cubes of side 2 cm. How many smaller cubes are formed?
18. A box with external dimensions of 50 cm × 40 cm × 30 cm is made of wood 2 cm thick. Find the volume of the wood used.
19. A sphere is melted and recast into 64 smaller spheres of equal size. If the radius of the original sphere is 8 cm, find the radius of each smaller sphere.
20. A cylindrical vessel has a base radius of 10 cm and height of 30 cm. It is filled with water. If a solid sphere of radius 7 cm is submerged into it, find the rise in water level.

Mensuration in 2D

21. Find the area of a trapezium whose parallel sides are 15 cm and 10 cm, and the distance between them is 8 cm.
22. A rhombus has diagonals measuring 12 cm and 16 cm. Find its area.
23. A rectangle has a length of 20 cm and a width of 15 cm. Calculate its diagonal.
24. A triangle has a base of 18 cm and a height of 12 cm. Calculate its area.
25. A circle has a radius of 14 cm. Find its area and circumference.
26. A regular hexagon is inscribed in a circle with a radius of 10 cm. Find the area of the hexagon.
27. A square has a diagonal of 10 cm. Find its area.
28. A parallelogram has a base of 25 cm and a height of 12 cm. Calculate its area.
29. A kite has diagonals of 14 cm and 18 cm. Find its area.
30. The radius of a semicircle is 7 cm. Calculate its perimeter and area.

Real-World Applications

31. A dam releases 200 cubic meters of water every second. How much water is released in an hour?
32. A swimming pool is 25 m long, 10 m wide, and 2 m deep. Calculate its capacity in liters.
33. A cylindrical drum with a base radius of 35 cm and a height of 1.5 m is used to store oil. Find its capacity in liters.
34. A farmer has a field in the shape of a trapezium with parallel sides of 50 m and 30 m, and a height of 40 m. Find the area of the field.
35. A cylindrical well has a diameter of 4 m and a depth of 20 m. Find the volume of earth dug out.
36. A metallic wire is bent to form a circle with a radius of 14 cm. Find the length of the wire.
37. A rectangular hall with dimensions 12 m × 8 m is to be carpeted. Find the cost of carpeting at Rs. 250 per square meter.
38. A conical tent has a base radius of 7 m and a height of 24 m. Find the area of the canvas required to make the tent.
39. A cylindrical pillar with a radius of 2 m and a height of 10 m is to be painted. Find the cost of painting it at Rs. 8 per square meter.
40. A cuboidal room is 12 m long, 8 m wide, and 6 m high. It has one door of size 2 m × 1 m and two windows of size 1.5 m × 1 m each. Find the cost of painting the walls at Rs. 50 per square meter.

Additional Practice Questions

41. A rectangular garden is 50 m long and 30 m wide. Find the cost of fencing it at Rs. 15 per meter.
42. A metallic cone with a radius of 10 cm and height of 24 cm is melted and recast into spheres of radius 2 cm. How many spheres are formed?
43. A tank with a square base of side 4 m and height 3 m is filled with water. If the tank is tilted, find the maximum height to which the water can rise.
44. A wheel with a diameter of 1 m makes 200 revolutions. Calculate the distance covered by the wheel.
45. A pipe of length 5 m and internal diameter 10 cm is full of water. Find the volume of water it can hold.
46. A cubical box with a side length of 3 m is completely filled with sand. How many smaller cubes of side 1 m can be formed from it?
47. The diameter of a circle is increased by 20%. Find the percentage increase in its area.
48. A square is inscribed in a circle of radius 7 cm. Find the area of the square.
49. A regular pentagon has a side length of 6 cm. Find its perimeter and area.
50. A hollow sphere has an outer radius of 10 cm and an inner radius of 8 cm. Find its surface area.