R'Man;
Thanks for the compliment. My math skills are nowhere near yours though. During my working career as a machinist outside of just plain arithmetic I used more trig than anything. Trig of course doesn't come into play here.
I had just assumed that taking that median diameter times half the metal removed from the diameter differences would be a close approximation. had not realized it would in fact be exact.

Miller/TN
I Didn't Say Everything I Said, Yogi Berra