Compute $\iint _ { S } \vec { F } \cdot \vec { n } d S$

Multiple Choice

Compute $\iint _ { S } \vec { F } \cdot \vec { n } d S$ where S is the unit sphere, $\vec { n }$ is the unit outward normal, and $\vec { F } ( x , y , z ) = \left\langle x , y , z ^ { 2 } \right\rangle$

A) $\frac { 12 } { 3 } \pi$
B) $\frac { 8 } { 3 } \pi$
C) $\frac { 4 } { 3 } \pi$
D) $\frac { 1 } { 3 } \pi$