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\includegraphics[max width=\textwidth, alt={}, center]{22a31966-4433-4d7d-8a75-bcd536acfa24-3_646_841_593_651} The diagram shows part of the graph of \(y = \frac { 18 } { x }\) and the normal to the curve at \(P ( 6,3 )\). This normal meets the \(x\)-axis at \(R\). The point \(Q\) on the \(x\)-axis and the point \(S\) on the curve are such that \(P Q\) and \(S R\) are parallel to the \(y\)-axis.

1. Find the equation of the normal at \(P\) and show that \(R\) is the point ( \(4 \frac { 1 } { 2 } , 0\) ).
2. Show that the volume of the solid obtained when the shaded region \(P Q R S\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis is \(18 \pi\).