What practical applications had the number pi in the ancient worlds and what was the motivation for calculating it? I know that modern sciences have many many applications for the number PI, many of them outside of geometry, but I do not understand what practical applications had this constant in the ancient world.
What motivated the Greeks, Babylonians and the Egyptians to try to calculate this number?

If you are interested in the volume of a heap of wheat (which looks like a cone) or in the content of a granary (which may look like a cylinder), then you need approximations of $\pi$. The Babylonians used $\pi = 3$ in plane geometry, and the approximation $\pi = 3 \frac18$ only occurs in connection with computing the volume of solids. 
