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

Use spherical coordinates to find the volume of the solid that lies above the cone z^{2}= x^{2}+ y^{2}and below the sphere x^{2}+ y^{2}+ z^{2}= z

2. Relevant equations

I'm going to use { as an integral sign.

Volume = {{{ P^{2}Sin[Φ] dP dΦ dΘ

3. The attempt at a solution

P^{2}= x^{2}+y^{2}+z^{2}

P^{2}= z

P = Sqrt[z]

(P Cos[Φ])^{2}= P^{2}Sin^{2}[Φ]

Cos^{2}[Φ] = Sin^{2}[Φ]

Tan^{2}[Φ] = 1

Φ = Pi/4

And for the limits of integration i got:

from 0 to 2 Pi on the first integral bracket

from 0 to Pi/4 on the second integral bracket

from 0 to Sqrt[z] on the thrid integral bracket

I was hoping someone could please confirm that these are the right limits of integration before i evaluate it, thanks in advanced!

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# Homework Help: Finding the volume with a triple integral

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