Editing Archimedes (section)

==== ''On the Sphere and Cylinder'' ====
{{Main|On the Sphere and Cylinder}}
[[File:Esfera Arquímedes.svg|thumb|A sphere has 2/3 the volume and surface area of its circumscribing cylinder including its bases|209x209px]]
In this two-volume treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a [[sphere]] and a [[circumscribe]]d [[cylinder (geometry)|cylinder]] of the same height and [[diameter]]. The volume is {{sfrac|4|3}}{{pi}}{{math|''r''}}<sup>3</sup> for the sphere, and 2{{pi}}{{math|''r''}}<sup>3</sup> for the cylinder. The surface area is 4{{pi}}{{math|''r''}}<sup>2</sup> for the sphere, and 6{{pi}}{{math|''r''}}<sup>2</sup> for the cylinder (including its two bases), where {{math|''r''}} is the radius of the sphere and cylinder.