Question

A sphere of maximum volume is cut-out from a solid hemisphere of radius r, what is the ratio of the volume of the hemisphere to that of the cut-out sphere?

Answer 1

Since, a sphere of maximum volume is cut out from a solid hemisphere of radius.

i.e., radius of sphere

Therefore,

The volume of sphere

…… (i)

The volume of hemisphere …… (ii)

Divide (i) by (ii).