Find the Area of the Surface Generated by Revolving the Curve

Multiple Choice

Find the area of the surface generated by revolving the curve about the y-axis. $$y = 169 - x ^ { 2 } , 0 \leq x \leq 13$$

A) $\frac { 114,245 ^ { \frac { 3 } { 2 } } - 1 } { 12 } \pi$
B) $\frac { 677 ^ { \frac { 3 } { 2 } } - 1 } { 12 } \pi$
C) $\frac { 114,245 ^ { \frac { 3 } { 2 } } - 1 } { 6 } \pi$
D) $\frac { 114,245 ^ { \frac { 3 } { 2 } } - 1 } { 3 } \pi$
E) $\frac { 677 ^ { \frac { 3 } { 2 } } - 1 } { 6 } \pi$