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

Use a triple integral to find the volume of solid enclosed between the sphere and paraboloid.

2. Relevant equations

Equation for sphere x^{2}+y^{2}+z^{2}=2a^{2}

Equation for paraboloid az = x^{2}+y^{2}(a>0)

3. The attempt at a solution

Trying to find limits of integration:

For integration of dz, rearranging the both equation in terms of z, the limits are from

z= 1/a (x^{2}+y^{2}) to

z= SQRT (2a^{2}- x^{2}- y^{2})

Next i suppose i should find the equations in xy plane by solving the given equations simultaneously to determine where the sphere and paraboloid intersect. When i equate both equation, i got this expression

2a^{4}= (x^{2}+y^{2})^{2}+a^{2}(x^{2}+y^{2}). I got stuck here as I do not know how to find the limits for dx and dy. Do i need to use polar coordinates or sphere coordinates? Can anyone explain these to me? Thanks

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# Homework Help: Triple integral to find Volume of Solid

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