To expand search, see The Measurement of Area and Volume. For material on related topics, see Calculus. Laterally related topics: Archimedes' Method and Limit.
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Fletcher, E. N. R. The area of the curved surface of a hemisphere in ancient Egypt. Math. Gaz. 54 (1970), no. 389, 227--229. SC: 01A15, MR: 58 #9987.
Problem 10 of the Moscow papyrus discusses the surface area of a basket and is thought by some to compute the surface area of a hemisphere. The author analyzes which units may have been used in the problem, and advances the theory that the basket in question was, in fact, hemispherical, and was designed to hold 100 Hekat of corn. He notes that the units used in ancient Egypt appear to have some interesting geometrical properties. For example, a circle with a radius of 1 pes (or "foot", equal to 16 digits) was approximately equal in area to a square with sides measuring 1 royal cubit. These are all fascinating possibilities. Closely related topics: Ancient Egypt, The Sphere, and The Measurement of Area and Volume.