9
\includegraphics[max width=\textwidth, alt={}, center]{d6976a4b-aecf-43f1-a3f2-bcad37d03585-12_764_967_292_555}
The diagram shows the curve with equation \(y = \sqrt { 2 x ^ { 3 } + 10 }\).
- Find the equation of the tangent to the curve at the point where \(x = 3\). Give your answer in the form \(a x + b y + c = 0\) where \(a , b\) and \(c\) are integers.
\includegraphics[max width=\textwidth, alt={}, center]{d6976a4b-aecf-43f1-a3f2-bcad37d03585-12_2716_35_141_2013} - The region shaded in the diagram is enclosed by the curve and the straight lines \(x = 1 , x = 3\) and \(y = 0\).
Find the volume of the solid obtained when the shaded region is rotated through \(360 ^ { \circ }\) about the \(x\)-axis.