Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

Multiple Choice

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ where $\mathbf { F } = ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$ and S is the part of the surface $z = 1 - x ^ { 2 } - y ^ { 2 }$ that lies above the $x y -$ plane and has upward orientation.

A) $- 3 \pi$
B) $- \frac { 3 \pi } { 4 }$

C) $- \frac { 3 \pi } { 2 }$
D) $1$
E) $3 \pi$
F) $\frac { 3 \pi } { 4 }$
G) $\frac { 3 \pi } { 2 }$
H) $\frac { 4 \pi } { 3 }$