# How do I calculate the volume of the intersection of a cylinder with a not concentric sphere?

I have, in metal, cut a $1.5''$ radius hemisphere (left half); now I want to cut a $1.8''$ diameter cylinder at $120^\circ$ from the horizontal and $0.333''$ deep on one edge and $0.031''$ deep at the other (referred to the edge of the hemisphere), with its' axis crossing the horizontal reference $0.226''$ to the left of the center of the hemisphere. I need to be able to calculate the amount of metal removed.

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I have trouble interpreting and visualizing your specification. An illustration might help. –  MvG Oct 8 '12 at 9:44