An ice-cream cone consists of a right circular cone of height 14cm and diameter of the circular top is 5 cm. It has hemisphere on the top with the same diameter as of circular top. Find the volume of ice-cream in the cone.

A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 14 cm, and the total height of the vessel is 13cm. Find the inner surface area of the vessel.

From a circular cylinder of base diameter 10cm and height 12cm, a conical cavity with the same base and height is carved out. Find the volume of the remaining solid.

A student was asked to make a model in his workshop, which shaped like a cylinder with two cones attached at its two ends, using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 10 cm. If each cone has a height of 2cm, find the volume of air contained in the model. (Consider the outer and inner dimensions of the model to be nearly the same).

A decorative block as shown in the given figure is made of a cube and a hemisphere. The edge of the cube is 10cm, and the radius of the hemisphere attached on the top is 3.5. Find the cost of painting the block at the rate of 50 paise per sq.cm.