1.22: Past-paper question 11

Figure 5 shows part of the curve $\displaystyle C$ with equation $\displaystyle y = \sqrt{4x - 8}$ and the line $\displaystyle l$ with equation $\displaystyle x = b$ where $\displaystyle b > 0$

The finite region bounded by the curve $\displaystyle C$, the $\displaystyle x$-axis and the line $\displaystyle l$, shown shaded in Figure 5, is rotated through $\displaystyle 360^\circ$ about the $\displaystyle x$-axis.

Given that the volume of the solid formed is $\displaystyle 50\pi$ units3

find the value of $\displaystyle b$