Looked into unwrap for a cone, and used MoI to make a sketch of some of the mathematics.
Unwrap gives the circumference length of a circle. Flow of the unwrap line to a circle with the slant height radius "s" creates the unwrapped base.
The formulas are also said to work for cylinders. The conical frustrum is a cone with the "top" cut off.

Two references are archaeological. The papers are free on the internet.

Unwrapping Highly-Detailed 3D Meshed of
Rotationally Symmetric Man-Made Objects
Bastian Rieck, Hubert Mara, and Susanne Kr..omker

Rollouts of Fine Ware Pottery using High Resolution 3D Meshes
S. Bechtold and S. Krömker and H. Mara and B. Kratzmüller

Unwrapping Curves from Cylinders and Cones
Tom M. Apostol and Mamikon A. Mnatsakanian

May try to do a script.

- Brian