AMC 12 2017a 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 \textbf{(B)}\ 12 \textbf{(C)}\ 18 \textbf{(D)}\ 20 \textbf{(E)}\ 24