Practice Mensuration (Area & Volume) Practice Questions with Detailed Solutions – Level 2

A solid metallic sphere of radius 6 cm is melted and recast into a solid right circular cone whose base radius is 6 cm. What is the height of the cone?

A cylindrical vessel of radius 14 cm contains some water. A solid sphere of radius 7 cm is dropped into it and is fully submerged. By how much does the water level rise?

The radius of a right circular cylinder is increased by 20% and its height is decreased by 20%. What is the percentage change in its volume?

A solid right circular cone has base radius 7 cm and height 24 cm. What is its total surface area? (Use \(\pi = \dfrac{22}{7}\))

The total surface area of a solid hemisphere is 462 cm². What is its volume? (Use \(\pi = \dfrac{22}{7}\))

A bucket is in the shape of a frustum of a cone. The radii of its circular ends are 14 cm and 7 cm, and its height is 6 cm. What is its capacity? (Use \(\pi = \dfrac{22}{7}\))

The length of the diagonal of a cube is \(6\sqrt{3}\text{ cm}.\) What is the total surface area of the cube?

The areas of three adjacent faces of a cuboid are \(24 \text{ cm}^{2}\), \(32 \text{ cm}^{2}\) and \(48 \text{ cm}^{2}\). What is the volume of the cuboid?

A solid metallic cylinder of diameter 6 cm and height 8 cm is melted and recast into spherical bullets, each of diameter 2 cm. How many bullets can be made?

The surface area of a sphere increases by 44%. By what percentage does its volume increase?