2017 AMC 10A Problem 11

The region consisting of all points in three-dimensional space within 3 units of line segment \overline{AB} has volume 216\pi. What is the length \textit{AB}?

\textbf{(A)}\ 6\qquad\textbf{(B)}\ 12\qquad\textbf{(C)}\ 18\qquad\textbf{(D)}\ 20\qquad\textbf{(E)}\ 24

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.