Write True or False and justify your answer in each of the following:
The volume of the largest right circular cone that can be fitted in a cube whose edge is $2r$ is equal to the volume of a hemisphere of radius $r$.

(A) The edge of the cube is $2r$. The largest right circular cone that can be fitted inside this cube will have a height $h = 2r$ and a base diameter equal to the edge of the cube,so the radius of the cone is $R = r$.
The volume of this cone is given by $V_{cone} = \frac{1}{3} \pi R^2 h = \frac{1}{3} \pi (r)^2 (2r) = \frac{2}{3} \pi r^3$.
The volume of a hemisphere of radius $r$ is given by $V_{hemisphere} = \frac{2}{3} \pi r^3$.
Since the volume of the cone is $\frac{2}{3} \pi r^3$ and the volume of the hemisphere is $\frac{2}{3} \pi r^3$,the volumes are equal.
Hence,the given statement is True.