(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A solid lies above the cone [tex]z=\sqrt{x^2+z^2}[/tex] and below the sphere [tex]x^2+y^2+z^2=z[/tex]. Describe the solid in terms of inequalities involving spherical coordinates.

2. Relevant equations

In spherical coordinates, [tex]x=\rho\sin\phi\cos\theta[/tex], [tex]y=\rho\sin\phi\sin\theta[/tex], and [tex]z=\rho\cos\phi[/tex]

3. The attempt at a solution

I have no idea how to do this problem. My attempts have involved converting the two given equations to spherical coordinates, at which point everything is very messy and I don't know where to go next.

I've attached a couple of 3D graphs to help with visualization.

The answer is supposed to be [tex]0\leq\phi\leq\frac{\pi}{4}[/tex] and [tex]0\leq\rho\leq\cos{\phi}[/tex], but this doesn't make much sense to me.

Any help would be great. Thanks!

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# Homework Help: Describing a Solid in Spherical Coordinates

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