Find the Volume of the Solid Generated by Revolving the Region

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the curve $y = \ln x$ , the $x$ -axis, and the vertical line $\mathrm { x } = \mathrm { e } ^ { 2 }$ about the $\mathrm { x }$ -axis.

A) $\pi ( e - 1 )$
B) $\pi \mathrm { e }$
C) $\pi \left( e ^ { 2 } - 1 \right)$
D) $2 \pi \left( e ^ { 2 } - 1 \right)$