I have, in metal, cut a 1.5" radius hemisphere (left half); now I want to cut a 1.8" diameter cylinder at 120 degrees from the horizontaland 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 centre of the hemisphere. I need to be able to calculate the amount of metal removed
Construct the hemisphere and the cylinder in any decent 3D CAD system (even a free one), and intersect them. Then ask the CAD system to calculate the volume of the intersection. Like MvG, I can't really understand what shape you're describing, so I can't do the construction myself.