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\includegraphics[max width=\textwidth, alt={}, center]{c8ac31bc-0f76-4d00-a28b-4a07758f9663-16_611_529_260_808} The diagram shows part of the curve with equation \(y = \sqrt { } \left( x ^ { 3 } + x ^ { 2 } \right)\). The shaded region is bounded by the curve, the \(x\)-axis and the line \(x = 3\).

1. Find, showing all necessary working, the volume obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.
2. \(P\) is the point on the curve with \(x\)-coordinate 3 . Find the \(y\)-coordinate of the point where the normal to the curve at \(P\) crosses the \(y\)-axis.