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.
- $\mathbf { F } ( x , y , z ) = x z i + y z j + k , S$ is the cap cut from the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ by the plane $z = 3$ , direction is outward

A) $\frac { 63 } { 2 } \pi$
B) $- \frac { 63 } { 2 } \pi$
C) $\frac { 35 } { 2 } \pi$
D) $63 \pi$