Question

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

Answer 1

Let the radius of the hemisphere = r units

Radius of the cone = radius of the hemisphere

height of the cone = radius of the hemisphere

h = r ----( 1 )

Therefore ,

Required

maximum volume of the cone = $\frac{1}{3}\times \pi r^{2}h$

V =$\frac{1}{3}\times \pi r^2\times r$

=$\frac{1}{3}\times \pi r^3$cubic units