3
\includegraphics[max width=\textwidth, alt={}, center]{b6ae63ce-a8a8-45ef-9c75-2fab30de8ad9-2_497_1106_554_515} The diagram shows part of the curve \(x = \frac { 12 } { y ^ { 2 } } - 2\). The shaded region is bounded by the curve, the \(y\)-axis and the lines \(y = 1\) and \(y = 2\). Showing all necessary working, find the volume, in terms of \(\pi\), when this shaded region is rotated through \(360 ^ { \circ }\) about the \(y\)-axis.