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^2h $. If we look at the changes in volume and height in just one hour, we can solve for the radius. \begin{align*} \pi r^2h_f-\pi r^2h_0&=V_f-V_0\quad\Rightarrow\\ \pi r^2(\Delta h)&=\Delta V\quad\Rightarrow\\ \pi r^2(4)&=20\pi\quad\Rightarrow\\ 4r^2&=20\quad\Rightarrow\\ r^2&=5 \end{align*} Since the radius must be positive, $ r=\boxed{\sqrt{5}} $ meters.