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

Use polar coordinates to find the volume of the given solid.

Inside the sphere x²+y²+z²=16 and outside the cylinder x²+y²=4.

2. Relevant equations

x=rcosΘ,y=rsinΘ, x²+y²=r²

3. The attempt at a solution

2∫∫ (√(16-r²)r)drdΘ R{(r,Θ)l 0<Θ<2∏, 2<r<4}

I was wondering if this is the correct set up. I solved the equation for the sphere for z, and then substituted my x²+y², and I used that as the function which I want to integrate under because Its the function that goes the highest. Then I figured that the radius was going from 2 to 4 because that is the radius of each of the shapes. I chose to go from 0 to 2pi because I know that I need to roatate 360 degrees. I multiplied by two because i know the functions are symmetric.

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# Homework Help: Polar Coordinate problem

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