Mensuration – Mixed Problems

Mensuration – Mixed Problems (WBBSE Class 10 Level)

1. Half of a cuboidal water tank with length of 2.1 m and breadth of 1.5 m is filled with water. If 630 litre of water is poured into the tank, calculate the increased height of water.
2. Height of a right circular cylinder is twice its radius. If the height were 6 times the radius, the volume would increase by 539 cubic decimetres. Calculate the cylinder’s height.
3. In a right circular conical tent, 11 persons can stay. Each person requires 4 m² of base area and 20 m³ of air. Determine the height of the tent.
4. How many spherical marbles of 1 cm radius can be made by melting a solid iron sphere of 8 cm radius?
5. The inner length, breadth and height of a tea box are 7.5 dcm, 6 dcm and 5.4 dcm respectively. If the weight of the box filled with tea is 52 kg 350 g, but empty it’s 3.75 kg, find the weight of 1 cubic decimetre of tea.
6. Two solid spheres of radii 1 cm and 6 cm are melted to form a hollow sphere with outer radius 9 cm. Find its inner radius.
7. The height of a right circular cone is twice its base radius. If the height were seven times the base diameter, its volume would have been 539 cm³ more. Find its height.
8. A cylindrical wooden log has a curved surface area of 440 dm². Given wood density is 3 kg/dm³ and the log weighs 18.48 quintals, find its diameter.
9. A hollow pipe has outer radius 5 cm and inner radius 4 cm. If its total surface area is 1188 cm², find the pipe’s length.
10. A hemispherical pot with internal radius 9 cm is full of water. The water is poured into cylindrical bottles (diameter 3 cm, height 4 cm). How many bottles are needed to empty the pot?
11. A right circular cone has a base diameter of 21 m and height 14 m. Find the cost to colour its curved surface at ₹1.50 per m².
12. A solid metallic cylinder of radius 7 cm and height 20 cm is melted and recast into spherical balls of radius 1 cm each. Find the number of balls formed.
13. A closed cylindrical drum is made of metal sheet, having diameter 1.4 m and height 2 m. Find the cost of making it at ₹150 per m².
14. A cube of edge 5 cm is cut into smaller cubes of edge 1 cm. Find the number of smaller cubes formed.
15. A solid metallic sphere of radius 10.5 cm is melted and recast into cones each having radius 3.5 cm and height 3 cm. Find the number of cones.
16. A hemispherical bowl of internal radius 7 cm is completely filled with milk. This milk is to be filled into cylindrical bottles of radius 3.5 cm and height 6 cm. Find the number of bottles required.
17. The diameter of a right circular cylinder is 28 cm and height is 2 m. Find the cost of painting its entire surface at ₹120 per m².
18. A solid sphere of radius 6 cm is melted and recast into smaller spheres of radius 2 cm each. Find the number of small spheres formed.