- #1

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## Homework Statement

Use polar coordinates to find the volume of the solid inside the hemisphere z=sqrt(16-x^2-y^2) and inside the cylinder x^2+y^2-4x=0

## Homework Equations

z=sqrt(16-x

^{2}-y

^{2})

x

^{2}+y

^{2}-4x=0

x=rcos(Θ)

y=rsin(Θ)

z=√(16-r

^{2})

## The Attempt at a Solution

∫∫ r√(16-r

^{2}) dr dΘ

The problem is the bounds; because the circle isn't centered it's throwing me off. Would dr be from 2 to 4? That's the start and end of the radius as it's a circle centered at (2,0) with a radius of 2. Of course I'm assuming that dΘ is from 0 to 2pi. I tried integrating with dr from 0 to 2 and from 2 to 4, but both times the answer was different than Wolfram's.