Let $E$ be the solid region that is above the cone $z=\sqrt[\phantom{2}]{x^2+y^2}$ and below the hemisphere $z=\sqrt[\phantom{2}]{9-x^2-y^2}.$ Use the Divergence Theorem to compute the flux of vec$(F)(x,y,z)=($:$x{z}^2,\frac{y^3}{3},z{x}^2$:$)$ outward across the boundary of $E.$

grad$*vec(F)=\frac{d}{d}(x{z}^2)+\frac{d}{d}(\frac{y^3}{2})+\frac{d}{1}(z{x}^2)$