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

Use spherical coordinates to find the volume of the solid bounded above by the sphere with radius 4 and below by the cone z=(x^2 + y^2)^(1/2).

2. Relevant equations

All general spherical conversions

Cone should be [tex]\phi[/tex]=[tex]\pi[/tex]/4

3. The attempt at a solution

So far I think the triple integral setup is

0[tex]\leq[/tex][tex]\rho[/tex][tex]\leq[/tex]4

0[tex]\leq[/tex][tex]\theta[/tex][tex]\leq[/tex]2[tex]\pi[/tex]

0<[tex]\phi[/tex][tex]\leq[/tex][tex]\pi[/tex]/4

My question is, for dV, do I need anything more than ([tex]\rho[/tex]^2)sin[tex]\phi[/tex]d[tex]\rho[/tex]d[tex]\theta[/tex]d[tex]\phi[/tex]? Or do I need to figure out the intersection and volume that describes the area bounded above by the sphere and below the cone? Or do I already have that with my limits and standard dV question? (if I am correct so far). Any help would be great. Thanks.

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# Homework Help: Need help setting up triple integral in spherical coordinates

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