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.
- $\mathbf { F } = x \mathbf { i } + y \mathbf { j } + z ^ { 3 } \mathbf { k }$ ; S is portion of the cone $z = 3 \sqrt { x ^ { 2 } + y ^ { 2 } }$ between $z = 3$ and $z = 6$ ; direction is outward

A) $- \frac { 1604 } { 5 } \pi$
B) $\frac { 1604 } { 5 } \pi$
C) $\frac { 802 } { 5 } \pi$
D) $- \frac { 802 } { 5 }$