Question: Problem 6: Let the surface S be the part of the cone \(z=\sqrt{{{x}^{2}}+{{y}^{2}}}\) that lies in the region \(0\le z\le 2\). Let F(x, y, z) be the vector field

\[\vec{F}\left( x,y,z \right)=xz\mathbf{i}+yz\mathbf{j}+z\mathbf{k}\]

Calculate the flux integral

\[\iint\limits_{S}{\vec{F}\cdot \vec{n}dS}\]

where n is the outward pointing unit normal on S.