2013 Gauss 8 Problem 14

A cube has a surface area of 54\,\text{cm}^2. The volume of the cube, in \text{cm}^3, is

\textbf{(A)}\ 81\quad \textbf{(B)}\ 343\quad \textbf{(C)}\ 18\quad \textbf{(D)}\ 27\quad \textbf{(E)}\ 729

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 Gauss contests here.