How to cut out hollow cylinder shape

I am attempting to cut out a hollow cylinder shape from within a solid cylinder.  A key requirement is that the two ends of the cut-out shape must have different diameters.  I have attached a drawing to show what I am aiming for.  The dashed area shows the shape I would like to cut out.  The bottom drawing shows the solid (blue) area and the cut-out (white) area.

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