Answer
$$V = \frac{{{\pi ^2}}}{2}$$
Work Step by Step
$$\eqalign{
& y = \sin x,{\text{ }}y = 0,{\text{ }}x = 0,{\text{ }}x = \pi \cr
& V = \pi \int_a^b {{{\left[ {R\left( x \right)} \right]}^2}} dx \cr
& {\text{Let }}R\left( x \right) = \sin x \cr
& {\text{So}},{\text{ the volume of the solid of revolution is}} \cr
& V = \pi \int_0^\pi {{{\left( {\sin x} \right)}^2}} dx \cr
& {\text{Using trigonometric identities}} \cr
& V = \pi \int_0^\pi {\frac{{1 - \cos 2x}}{2}} dx \cr
& {\text{Integrate}} \cr
& V = \frac{\pi }{2}\left[ {x - \frac{1}{2}\sin 2x} \right]_0^\pi \cr
& V = \frac{\pi }{2}\left[ {\pi - \frac{1}{2}\sin 2\pi } \right] - \frac{\pi }{2}\left[ {0 - \frac{1}{2}\sin 0} \right] \cr
& V = \frac{{{\pi ^2}}}{2} \cr} $$
