A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of the top which is open is 5 cm. It is filled with water up to the rim. When lead shots, each of which is a sphere of radius 0.5 cm, are dropped into the vessel, one-fourth of the water flows out. Find the number of lead shots dropped in the vessel.

A hemi-spherical bowl has negligible thickness and the length of its circumference is 198 cm. Find the capacity of the bowl.

The radii of the bases of two right circular cones of same height are r₁ and r₂ respectively. The cones are melted and recast into a solid sphere of radius R. Find the height of each cone in terms of r₁, r₂ and R.

A cone and a hemisphere have the same base and the same height. Find the ratio of their volumes.