Step by Step Solutions

(All Steps) Let \Sigma be the boundary of the solid bounded above by the sphere x^2+y^2+z^2=2 z and below by the cone √3 z=√x^2+y^2. Evaluate

Question: Let \(\Sigma\) be the boundary of the solid bounded above by the sphere

\[x^{2}+y^{2}+z^{2}=2 z\]

and below by the cone \(\sqrt{3} z=\sqrt{x^{2}+y^{2}}\). Evaluate

\[\iint_{\Sigma} \vec{F} \cdot \vec{n} d S\]

if \(\vec{n}\) is the outward normal and \(\vec{F}(x, y, z)=6 x \vec{i}-3 y \vec{j}+\sqrt{x^{2}+y^{2}} \vec{k}\).

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