2017 AMC 12A Problem 8

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 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.