Evaluate ${}_{}$vec$(F)*vec(n)dS,$ where vec$(F)=x^2$vec$(i)+y^2$vec$(j)+z^2$vec$(k)$ and $$ is the cone $z=\sqrt[\phantom{2}]{x^2+y^2}$ for $x^2+y^{2}2,$ together with the top cap consisting of the points $(x,y,\sqrt[\phantom{2}]{2})$ with $x^2+y^{2}2.$