Calculus
# Volume of Revolution

$\begin{array}{c}&y= 18\sin x - a \ (0 < a \ < 18), &x=0, &x=\pi, &y=0 .\end{array}$ What is the value of $a$ that minimizes the volume of the solid obtained by rotating the region around the $x$-axis?

The yellow-colored region in the above diagram is bounded by