(a)[5]
Determine the equation of the tangent to the curve at the point where $x = 3$. Write your answer in the form $ax + by + c = 0$ where $a$, $b$ and $c$ are integers.
(b)[3]
The shaded region in the diagram is bounded by the curve and the straight lines $x = 1$, $x = 3$ and $y = 0$. Find the volume of the solid formed when the shaded region is turned through $360^\circ$ about the $x$-axis.