1.13: Figure 2 shows the graph of part of the curve with equation .

Figure 2 shows the graph of part of the curve $\displaystyle C$ with equation $\displaystyle y = \sqrt{2x + 6}$. The finite region enclosed by the curve $\displaystyle C$ and the straight line with equation $\displaystyle 3y - x = 3$ is rotated through $\displaystyle 360^\circ$ about the $\displaystyle x$-axis.

Use algebraic integration to find the exact volume of the solid generated. Give your answer in terms of $\displaystyle \pi$