Question

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

Answer 1

Clearly,
Radius of the base of cone = Radius of the hemisphere $=r$

Height of cone = Radius of the hemisphere

Volume of the cone $\frac{1}{3}\pi \times {\left(r\right)}^2\times r=\frac{1}{3}\pi \times {\left(r\right)}^3$