Calippo, toothpaste and milk .. packing

Solution 1:

The convex hull of a circle and a line segment is developable. I don't know if this is the unique developable surface with the given boundaries.

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(Ignore the extra chords drawn in the circle.)

I'm fairly sure that if you start with a cylinder and pinch it flat at both ends, a perfectly flat tetrahedron is the only developable surface you can get. The curved nature of the real-world milk cartons is because the material is slightly extensible (it has a coating of plastic to make it liquid-proof). Better intuition can be gained by trying the experiment with a sheet of plain paper instead.

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