Just for interest, I was taught by goldsmiths and silversmiths who made a lot of beautiful pieces as they were all ex Garrard the Crown Jewellers craftsmen. None of them used mathematical formulas when working out metal sizes. When making a bowl from a design, the disc size was calculated by just adding the diameter of the bowl's top to the depth of the bowl, so for a 6 inch bowl that was 3 inches deep we would cut a 9 inch disc. The shaped bowl would be then filed to it's required size when tidying up it's top edge.

James
James Miller FIPG.