2003 Pascal Problem 25

In the cube shown, L and K are midpoints of adjacent edges AD and AB. The perpendicular distance from F to the line segment LK is 10. What is the volume of the cube, to the nearest integer?

\textbf{(A)}\ 323\quad \textbf{(B)}\ 324\quad \textbf{(C)}\ 325\quad \textbf{(D)}\ 326\quad \textbf{(E)}\ 327

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