I wouldn't even know where to begin with this problem. Any suggestions?
The volume of a right circular cone is $\displaystyle V=\frac13\pi r^2h\text.$ It looks like you almost had it, but the given radius is $\displaystyle 5r,$ not $\displaystyle 5\pi\text.$
If you want to derive the formula, an easy way to do it is to position a right triangle such that its right angle is at the origin and its two legs along the $\displaystyle x$- and $\displaystyle y$-axes, and find the volume of the solid resulting from revolving the triangular region about one of the axes.