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) $2 \pi \left( e ^ { 2 } - 1 \right)$

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The Answer of 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) $2 \pi \left( e ^ { 2 } - 1 \right)$

Find the Volume of the Solid Generated by Revolving the Region