Answer
$V = 4\pi $
Work Step by Step
$$\eqalign{
& {\text{Let }}y = \frac{{\sin x}}{x}{\text{ for }}x > 0,{\text{ 1 for }}x = 0,{\text{ and }}y = 0,{\text{ }}x = 0,{\text{ }}x = \pi \cr
& {\text{Use the shell method about the }}y{\text{ - axis}} \cr
& V = 2\pi \int_a^b {x\left[ {f\left( x \right) - g\left( x \right)} \right]} dx \cr
& {\text{From the graph}} \cr
& {\text{Let }}f\left( x \right) = \frac{{\sin x}}{x}{\text{ and }}g\left( x \right) = 0{\text{ on the interval }}\left[ {0,\pi } \right],{\text{ then}} \cr
& V = 2\pi \int_0^\pi {x\left( {\frac{{\sin x}}{x} - 0} \right)} dx \cr
& V = 2\pi \int_0^\pi {\sin x} dx \cr
& {\text{Integrating}} \cr
& V = 2\pi \left[ { - \cos x} \right]_0^\pi \cr
& V = 2\pi \left[ { - \cos \pi + \cos 0} \right] \cr
& {\text{Simplifying}} \cr
& V = 2\pi \left( {1 + 1} \right) \cr
& V = 4\pi \cr} $$
