
 Calculating Simple Volumes 
  The simple formula for the volume of a sphere was not known in antiquity, and it was a struggle to develop it. 
  Naturally, the sum total of the volumes in all the disks is not exactly the same as the volume of the sphere, (there are bits due to the curved edge of the sphere that are not included in the disks) but if we make the slices very very thin, the approximation becomes better and better. 
  Indeed, if we take a limit, as the number of slices, n, goes to infinity, we expect to obtain a definite integral, much in the same way as it was obtained in problems involving the dissection of an irregular area into a set of rectangles. 
 www.ugrad.math.ubc.ca /coursedoc/math101/notes/applications/volume.html (892 words) 
