How do I find the volume of the part of the equation $(z+3)^2+y^2+x^2=25$ that lies above the $xy$-plane? I know that you have to use double (iterated) integrals and polar coordinates.
2026-03-26 22:55:20.1774565720
What is the volume of the part of the equation $(z+3)^2+y^2+x^2=25$ that lies above the $xy$-plane?
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Let $z=0$ in $$(z+3)^2+y^2+x^2=25$$ to find the intersection of the sphere with the $xy$ plane.
We get $$x^2+y^2=16$$
Thus the integral in polar coordinates is $$\int_{0}^{2\pi} \int _{0}^{4} (-3+\sqrt {25-r^2})rdrd\theta$$