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I have to find the volume given by $z=2-\sqrt{x^2 + y^2}$ and $(x-1)^2 + y^2 = 1$. It looks like I should by using cylindrical coordinates, but I don't know what to do about $(x-1)$. Could you please give me some hints?

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There has to be something missing. The first equation describes a paraboloid, and the second describes a cylinder, and the "axes" of both are parallel. That means the volume in their intersection is going to be infinite as you travel in the direction of the negative $z$ axis. Or did you mean the volumes of them one at a time? In that case you still need to give another boundary, or else the volume is infinite... – rschwieb Feb 5 at 19:08

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