6 Fig. 6 shows the region enclosed by part of the curve \(y = 2 x ^ { 2 }\), the straight line \(x + y = 3\), and the \(y\)-axis. The curve and the straight line meet at \(\mathrm { P } ( 1,2 )\).
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{0a6247c9-ba64-4a8f-9e10-83986136cf56-2_643_933_1667_607}
\captionsetup{labelformat=empty}
\caption{Fig. 6}
\end{figure}
The shaded region is rotated through \(360 ^ { \circ }\) about the \(y\)-axis. Find, in terms of \(\pi\), the volume of the solid of revolution formed.
[0pt]
[You may use the formula \(V = \frac { 1 } { 3 } \pi r ^ { 2 } h\) for the volume of a cone.]
Section B (36 marks)