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

The textbook I have is horrible in explaining this stuff in the chapter so please bare with me.

So we have the information: Find the volume V inside both the sphere x^2 + y^2 + z^2 = 1 and the cone z =sqrt(x^2 + y^2)

2. Relevant equations

Where the heck do I began? I know this will require triple integration in spherical coordinates and the solution is (2/3)*pi*1^3(1-1/sqrt(2))

3. The attempt at a solution

I know the theta integrand is (0,2pi) because there are no bounds, but I have no idea where to find the limits of integration for the phi and zenith integrands. :(

EDIT (1): Just solved for the intersections of the sphere and cone and got z = 1/sqrt(2))

EDIT (2): Since phi = 1 and z = (1/sqrt(2)), it's safe to conclude that the zenith angle is pi/4...but what would be it's upper limit?

EDIT (3): I believe the limits for phi is 0 to pi/4. But I'm not quite sure why though? I think I got the integrands all figured out. I believe it's: for p = (0,1), phi = (0, pi/4) and theta = (0,2pi).

So overall, could someone just briefly explain to me why phi's limits of integration is from 0 to pi/4. thanks a bunch :D

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# Find the volume: once more

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