- #1
ryantc
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Homework Statement
1. Use polar coordinates to find the volume of the given solid.
2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
2. The attempt at a solution
My attempt as following:
2<=r<=4, and 0<=theta<=2pi
So I do a double integral of f(x,y)=sqrt(16-r^2)r dr d(theta) and it gives me 16sqrt(3)pi
but I saw the answer somewhere, the volume is 2 times the answer I got, I cannot figure out why 2 times? and in the answer it says "by symmetry", any explanation will be appreciated.