Use the divergence theorem to evaluate the surface integral ${}_{S}F*NdS$ where $F=10x{y}^{2}zi+10y{x}^{2}zj+z^{2}k,S$ is the closed hemispherical surface $z=\sqrt[\phantom{2}]{1-x^2-y^2}$ together with the disk $x^2+y^{2}1$ in the $xy-$plane, and $N$ is the outward unit normal for $S.$Use the divergence theorem to evaluate the surface integral ${}_{S}F*NdS$ where $F=10x{y}^{2}zi+10y{x}^{2}zj+z^{2}k,S$ is the closed hemispherical surface $z=\sqrt[\phantom{2}]{1-x^2-y^2}$ together with the disk $x^2+y^{2}1$ in the $xy-$plane, and $N$ is the outward unit normal for $S.$