Rhombus $ABCD$, with side length $6$, is rolled to form a cylinder of volume $6$ by taping $\overline{AB}$ to $\overline{DC}$. What is $\sin(\angle ABC)$? $\mathrm {(A)} \frac{\pi}{9}\qquad$ $ \mathrm {(B)} \frac{1}{2}\qquad$ $ \mathrm {(C)} \frac{\pi}{6}\qquad$ $ \mathrm {(D)} \frac{\pi}{4}\qquad$ $ \mathrm {(E)} \frac{\sqrt{3}}{2}$