jmc

The volume of the water increases by $20\pi$ cubic meters each hour, while the height of the water in the tank rises by 4 meters each hour. The volume of a right cylinder is $\pi r^{2}h$. If we look at the changes in volume and height in just one hour, we can solve for the radius. $$\begin{array}{rl}\pi r^2{h}_f-\pi r^2{h}_0& =V_f-V_0\Rightarrow \\ \pi r^2(\Delta h)& =\Delta V\Rightarrow \\ \pi r^2(4)& =20\pi \Rightarrow \\ 4r^2& =20\Rightarrow \\ r^2& =5\end{array}$$ Since the radius must be positive, $r=\boxed{\sqrt{5}}$ meters.