Let $\mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$

Multiple Choice

Let $\mathbf { F } ( x , y , z ) = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$ and S is $z = 9 - x ^ { 2 } - y ^ { 2 } , z \geq 0$ in the first octant. Then the flux of $\text { F }$ through S is

A) $\frac { 284 \pi } { 9 }$
B) $\frac { 243 \pi } { 8 }$
C) $\frac { 243 \pi } { 5 }$
D) $\frac { 224 \pi } { 3 }$
E) $\frac { 218 \pi } { 3 }$