Verify the Divergence Theorem by Evaluating $\iint _ { S } \mathbf { F } \cdot \mathbf { N } d s$

Multiple Choice

$\text { Let } F ( x , y , z ) = 2 x \hat { \mathbf { i } } - 2 y \hat { \mathbf { j } } + z ^ { 2 } \hat { \mathbf { k } } \text { and let } S \text { be the cylinder } x ^ { 2 } + y ^ { 2 } = 4,0 \leq z \leq 3 \text {. }$ Verify the Divergence Theorem by evaluating $\iint _ { S } \mathbf { F } \cdot \mathbf { N } d s$ as a surface integral and as a triple integral.

A) $18 \pi$
B) $36 \pi$
C) $12 \pi$
D) $108 \pi$
E) $54 \pi$