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SW can only unfold 2 kinds of parts - sheet metal parts and sheet metal parts made with the lofted bend feature. You won't be able to do this with either.
How about an obvious solution rather than a clever one? How about you model what you want, and then take the surface area of it and add a little for joining areas? SW won't give you the shape, but you didn't ask for the flat shape, you asked for how much material.
Thanks, Matt. I was just wondering if anyone had done it before. I'll use SW to verify my calculations for surface area instead of trying to be too "clever".