The region $W$ lies between the spheres $x^2+y^2+z^2=1$ and $x^2+y^2+z^2=9$ and within the cone $z=\sqrt{x^2+y^2}$ with $z\ge 0$; its boundary is the closed surface, $S$, oriented outward. Find the flux of $\vec F= x^3\vec i+y^3\vec j+z^3\vec k$ out of $S$.

flux =