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I believe that this is the answer. If we model the roofline as a curve and then treat the roof as a surface of revolution, I believe that it produces the answer needed.
I meant a hemiellipsoid.
The "ring wall" plus hemisphere will get close, I think (considering relative sizes). Maybe Allan could tell us how critical it is to get an exact answer. I emailed him to let him know I started a thread on his problem.
Had that condition not been given, the solution would have been simple, as you had posted, Sir. The dome is not a perfect hemishphere. It resembles an ellipsoid.
I just received this email from "Allan":