When I saw some problems about innovation behind area of a circle in this site, I was wondering that about a sphere. We know volume of sphere is $\frac{4}{3}\pi\cdot r^3$ and surface area is $4\pi\cdot r^2$, but how did Archimedes find these relation? Of course we can find this relation using vector calculus with rigorous integration,but those days Newton wasn't born,right?!!!! Also you can measure area of circle by inscribing a polygon and then Think what would happen when side of polygon is too large, but for a sphere (a 3 dimensional object), that is difficult... Also when surface area come to picture, difficulty increase tremendously (a curved area is coming), then by what method he found out these relation which is so fundamental to geometry? What was his innovative idea for finding this relations?? Thank you.
2026-03-27 12:14:26.1774613666
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Innovation behind formula for surface area and volume of a sphere
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Archimedes developed the Law of of the Lever which used very thoughtfully.
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There is an argument from first principles using a geometric construction. You can see it here, for example: mathcentral.uregina.ca/QQ/database/QQ.09.01/rahul1.html