If the radius of a sphere is increased by 10%, prove that its volume will be increased by 33.1%.

The total surface area of a cylinder is 462 cm² and its curved surface area is one-third of its total surface area. Find the volume of the cylinder.

The length and breadth of a room are in a ratio 3 : 2. The cost of carpeting the room at Rs 25 per m² is Rs 1350 and the cost of papering the four walls at Rs 15 per m² is Rs 2580. If one door and two windows occupy 8m², find the dimensions of the room.

The surface area of a sphere of radius 5 cm is five times the area of the curved surface of a cone of radius 4 cm. Find the height and volume of the cone.

A rectangular tank measuring 5m × 4.5m × 2.1 m is dug in the centre of the field measuring 13.5m × 2.5 m. The earth dug out is spread over the remaining portion of the field. How much is the level of the field raised?