2013 Pascal Problem 22

A water tower in the shape of a cylinder has radius 10 m and height 30 m. A spiral staircase, with constant slope, circles once around the outside of the water tower. A vertical ladder of height 5 m then extends to the top of the tower. Which of the following is closest to the total distance along the staircase and up the ladder to the top of the tower?

\textbf{(A)}\ 72.6 \text{ m}\quad \textbf{(B)}\ 320.2 \text{ m}\quad \textbf{(C)}\ 74.6 \text{ m}\quad \textbf{(D)}\ 67.6 \text{ m}\quad \textbf{(E)}\ 45.1 \text{ m}

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 Pascal contests here.