Question

find the maximum volume of a cone that can be cut of a solid hemisphere of radius r

Answer 1

cone gain maximum volume when cone base is equal to hemisphere base
now base of cone =pi.r^2
hence radius of cone equal r
and height =r
hence cone volume =pi.r^2.h/3
=pi.r^3/3
hence cone volume =half of hemisphere volume

Answer 2

The maximum radius of the cone = radius of hemisphere
Maximum height of cone = Radius of hemisphere.

So radius of cone = r
Height = r

Volume of cone = 1/3 π r² h
= 1/3 π r² x r
= 1/3 π r³

∴ Volume of cone = 1/3 π r³