Question 1003b

The curve ${C}$ has equation ${y= \mathrm{e}^{\frac{1}{4}x} - 1}$ and the line ${l}$ has equation ${y=- 2 x + 2.}$

The region ${R}$ is bounded by ${C, l}$ and the ${y\textrm{-axis}.}$ Find the volume of the solid of revolution when ${R}$ is rotated ${2\pi}$ radians about the ${x\textrm{-axis}.}$
Leave your answer correct to 2 decimal places.