AMC 12 2007b Problem 19

Rhombus $ABCD$, with side length $6$, is rolled to form a cylinder of volume $6$ by taping $\overline{AB}$ to $\overline{DC}$. What is $\sin(\angle ABC)$?

$\mathrm {(A)} \frac{\pi}{9} \mathrm {(B)} \frac{1}{2} \mathrm {(C)} \frac{\pi}{6} \mathrm {(D)} \frac{\pi}{4} \mathrm {(E)} \frac{\sqrt{3}}{2}$