Answer
$\dfrac{\pi^2}{2}$
Work Step by Step
Since, the vertical slices solid are circular discs , so we will use the disk method to compute the volume of revolution of the curve.
The volume of revolution of the curve can be expressed as: $V=\pi \int_p^q [f(x)]^2 dx\\=\pi \int_0^{\pi} \sin^{2} x \ dx \\= \dfrac{\pi}{2} \int_0^{\pi/2} (1-\cos 2x) \ dx \\=\dfrac{\pi}{2} [x-\dfrac{\sin 2x}{2}]_0^{\pi} \\=\dfrac{\pi}{2} [\pi+\dfrac{\sin2 ( \pi)}{2}-0]\\=\dfrac{\pi^2}{2}$
