# How did Archimedes find the surface area of a sphere?

In school we are told that the surface area of a sphere is $4\pi$. Is it true that Archimedes found the surface area of a sphere using the Archimedes Hat-Box Theorem? Is there a simple proof for this theorem? Thank you.

Added: Does that kind of projection as mentioned in the Archimedes Hat-Box Theorem preserve the areas of any shape on the surface of the sphere?

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I think you should loo here u.cs.biu.ac.il/~tsaban/Pdf/mechanical.pdf. –  Norbert Feb 7 '12 at 23:43