Suppose $\vec{F}(x,y,z) = \langle x, y, 3 z \rangle$. Let $W$ be the solid bounded by the paraboloid $z = x^2 + y^2$ and the plane $z = 16.$ Let $S$ be the closed boundary of $W$ oriented outward.

(a) Use the divergence theorem to find the flux of $\vec{F}$ through $S.$
$\displaystyle \iint\limits_S \vec{F} \cdot d\vec{A} =$

(b) Find the flux of $\vec{F}$ out the bottom of $S$ (the truncated paraboloid) and the top of $S$ (the disk).
Flux out the bottom =
Flux out the top =