Using the Divergence Theorem, Find the Outward Flux of F $\mathbf { F } = 3 x y ^ { 2 } i + 3 x ^ { 2 } y j + 6 x y \mathbf { k } ;$

Multiple Choice

Using the Divergence Theorem, find the outward flux of F across the boundary of the region D.
- $\mathbf { F } = 3 x y ^ { 2 } i + 3 x ^ { 2 } y j + 6 x y \mathbf { k } ;$ D: the region cut from the solid cylinder $x ^ { 2 } + y ^ { 2 } \leq 9$ by the planes $z = 0$ and $z = 6$

A) $2916 \pi$
B) $729 \pi$
C) $\frac { 729 } { 2 } \pi$
D) $1458 \pi$