The maximum volume of a cone that can be cut out of a solid hemisphere of radius $\text{'}r\text{'}$  is

So, height (cone) $=$  radius (hemisphere)

$h=r$

Volume of cone that can be cut $=\frac{1}{3}\pi r^{2}h$

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

$=\frac{1}{3}\pi r^3$