Suppose vec$(F)(x,y,z)=($:$x,y,5z$:$).$ Let $W$ be the solid bounded by the paraboloid $z=x^2+y^2$ and the plane $z=25.$ Let $S$ be the closed boundary of $W$ oriented outward.

$($a$)$ Use the divergence theorem to find the flux of vec$(F)$ through $S.$

${}_S$vec$(F)*dvec(A)=$

$$

$($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 $=$