TITLE: Triple Integrals in Spherical Coordinates
QUESTION [5 upvotes]: Use spherical coordinates to to find the volume of a solid bounded above by
$x^2 + y^2 + z^2 = z$ and below by $z$ $=$ $\sqrt{x^2 + y^2}$

REPLY [3 votes]: Just hints for the limits:
$$V=4\int_{\phi=0}^{\pi/2}\int_{\theta=\pi/4}^{\pi/2}\int_{r=0}^{1/2} r^2\sin^2\theta dr d\theta d\phi$$ wherein $x^2+y^2+(z-1/2)^2=\frac{1}{4}$. See below: