Find the Flux of the Vector Field F Across the Surface

Multiple Choice

Find the flux of the vector field F across the surface S in the indicated direction.
- $\mathbf { F } = \frac { z ^ { 2 } } { 9 } \mathbf { k } ; \mathrm { S }$ is the upper hemisphere of $\mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } = 9$ ; direction is outward

A) $\frac { 9 } { 2 } \pi$
B) $- \frac { 9 } { 2 } \pi$
C) $- \frac { 9 } { 2 }$
D) $\frac { 9 } { 2 }$