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

Multiple Choice

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , that is, find the flux of F across S. $\mathbf { F } ( x , y , z ) = - 5 z \mathbf { i } + 3 y \mathbf { j } - 5 x \mathbf { k }$ ; S is the hemisphere $z = \sqrt { 9 - x ^ { 2 } - y ^ { 2 } }$ ; n points upward.

A) $27$ $\pi$
B) 162
C) $54$ $\pi$
D) 162 $\pi$