Find the volume inside the sphere [tex]x^{2}+y^{2}+z^{z}=16[/tex] and outside the cylinder [tex]x^{2}+y^{2}=4[/tex]. Use polar coordinates.(adsbygoogle = window.adsbygoogle || []).push({});

The sphere's center lies at the origin. The region of integration is the base of the cylinder, the radius 2 xy disk [tex]x^{2}+y^{2}=4[/tex] and the two parts of the sphere are given by [tex]z=\pm\sqrt{16-x^{2}-y^{2}}[/tex]

Volume of sphere is 4 pi r^3 over 3 = 4 pi 4^3 over 3

Therefore:

Volume inside sphere but outside cylinder = [tex]\frac{4\pi 4^{3}}{3}-2\int_{0}^{2\pi}\int_{0}^{2}\left(\sqrt{16-r^{2}}\right)rdrd\theta[/tex]

What is wrong with my reasoning?

Thank you very much

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# Volume inside sphere, outside cylinder

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