Find the Surface Area Generated by Rotating the Lemniscate $r ^ { 2 } = 10 \cos 2 \theta$

Multiple Choice

Find the surface area generated by rotating the lemniscate $r ^ { 2 } = 10 \cos 2 \theta$ about the line $\theta = \pi$ .

A) $2 \pi \sqrt { 10 }$
B) $2 \pi \sqrt { 10 } ( 2 - \sqrt { 2 } )$
C) $\pi \sqrt { 10 }$
D) $\frac { \pi \sqrt { 10 } } { 10 }$
E) $\frac { \pi } { 10 }$