2021 Pascal Problem 22

Rectangle WXYZ has WX = 4, WZ = 3, and ZV = 3. The rectangle is curled without overlapping into a cylinder so that sides WZ and XY touch each other. In other words, W touches X and Z touches Y. The shortest distance from W to V through the inside of the cylinder can be written in the form \sqrt{\dfrac{a + b\pi^2}{c\pi^2}} where a, b and c are positive integers. The smallest possible value of a + b + c is

\textbf{(A)}\ 12\quad \textbf{(B)}\ 26\quad \textbf{(C)}\ 18\quad \textbf{(D)}\ 19\quad \textbf{(E)}\ 36

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.