2007 AMC 12B 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}\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}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.