Use the Shell Method to Find the Volume of the Solid

Multiple Choice

Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and
lines about the x-axis.
- $$\mathrm { x } = \frac { 1 } { 6 } \mathrm { e } ^ { 2 } , \mathrm { y } = 0 , \mathrm { x } = 0 , \mathrm { y } = 1$$

A) $\frac { \pi } { 6 } ( e - 1 )$
B) $6 \pi ( \mathrm { e } - 1 )$
C) $3 \pi \mathrm { e }$
D) $\pi ( e - 1 )$