Question

You have to make a trunk of a cone (i.e. cone with a cut-off tip) out of a 2m x 1m sheet of metal by cutting it out and wrapping it around. The diameter of the desired small opening is known (d=50mm) and the desired big opening has a known perimeter (P=2m). What are the measurements of this cut-out, in order to make maximum use of the sheet metal (i.e. max surface area)?
At a minimum, I'd like to know how to "unwrap" a circle in what looks like to me as an ellipse section.

Answer 1

The pic shows the basic idea. I have trouble unwrapping the thing and wrapping it back in 3D.