



 
Ron, By coincidence, an article appeared in the most recent issue of THE COLLEGE MATHEMATICS JOURNAL, 46:3 (May 2015), pages 162171, that clarifies what Archimedes did concerning volumes and areas, and what results were known long before him; the article is “Circular Reasoning: Who First Proved That C Divided by d Is a Constant?” by David Richeson. Most of the results you mention are in Euclid’s ELEMENTS, and were probably discovered much earlier. There you learn in Book 12 that
Euclid did not mention anything about the circumference of the circle, or of the surface area of a sphere. One of the many remarkable achievements of Archimedes (who came a generation or so after Euclid) was to prove that the same constant which we call pi equals
Of course, the volume of a cylinder is (3/2) times the volume of the sphere of the same radius (that is, the same as the radius of the base of the cylinder, while the height of the cylinder equals the diameter of the sphere), while the surface area of a cylinder (including its top and bottom) is also (3/2) times the surface area of the sphere with the same radius. According to Plutarch, Archimedes was so proud of his threehalves theorem, that he requested it be inscribed on his tomb. Chris  


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