Answer
$$\frac{\pi^{2}}{2}$$
Work Step by Step
Since the volume is given by
$$V=\pi \int_{a}^{b} f(x)^{2} d x$$
Then
\begin{align*}
V&=\pi \int_{0}^{\pi} \sin ^{2} x d x\\
&=\frac{\pi}{2} \int_{0}^{\pi}[1-\cos 2x]d x\\
&=\left.\pi\left(\frac{x}{2}-\frac{\sin 2 x}{4}\right)\right|_{0} ^{\pi}\\
&=\pi\left(\frac{\pi}{2}\right)\\
&=\frac{\pi^{2}}{2}
\end{align*}
