1999 Cayley Problem 18

A cylindrical pail containing water drains into a cylindrical tub 40 cm across and 50 cm deep, while resting at an angle of 45^\circ to the horizontal, as shown. How deep is the water in the tub when its level reaches the pail?

\textbf{(A)}\ 10\ \text{cm}\quad \textbf{(B)}\ 20\ \text{cm}\quad \textbf{(C)}\ 30\ \text{cm}\quad \textbf{(D)}\ 35\ \text{cm}\quad \textbf{(E)}\ 40\ \text{cm}

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.