Chapter 6.3, Problem 23ES

Consider the region to the right of the $y\text{-axis}$ , to the left of the vertical line $x=k\left(0<k<\pi \right)$ , and between the curve $y=\sin x$ and the $x\text{-axis}$ . Use a CAS to estimate the value of $k$ so that the solid generated by revolving the region about the $y\text{-axis}$ has a volume of $8$ cubic units.