Find the maximum volume of a cone that can be carved out of a solid hemisphere of radius r cm.

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.

The volume of a solid cylinder and a solid cone are same. If their radii are also same, the ratio between the heights of cylinder and cone is :

1. 3 : 1

2. 2 : 3

3. 1 : 3

4. 3 : 2