AMC 10 2017a 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 $\textit{AB}$? $\textbf{(A)}\ 6 \textbf{(B)}\ 12 \textbf{(C)}\ 18 \textbf{(D)}\ 20 \textbf{(E)}\ 24$