5
\includegraphics[max width=\textwidth, alt={}, center]{1b5d8cb1-fd1b-4fcf-8975-b5d020991c9a-2_570_1050_1393_550} The diagram shows part of the curve \(x = \frac { 8 } { y ^ { 2 } } - 2\), crossing the \(y\)-axis at the point \(A\). The point \(B ( 6,1 )\) lies on the curve. The shaded region is bounded by the curve, the \(y\)-axis and the line \(y = 1\). Find the exact volume obtained when this shaded region is rotated through \(360 ^ { \circ }\) about the \(\boldsymbol { y }\)-axis.