Editing Cylinder (section)

===''On the Sphere and Cylinder''===

[[File:Esfera Arquímedes.svg|thumb|right|A sphere has 2/3 the volume and surface area of its circumscribing cylinder including its bases]]
{{main|On the Sphere and Cylinder}}
In the treatise by this name, written {{Circa|225 BCE}}, [[Archimedes]] obtained the result of which he was most proud, namely obtaining the formulas for the volume and surface area of a [[sphere]] by exploiting the relationship between a sphere and its [[circumscribe]]d [[right circular cylinder]] of the same height and [[diameter]]. The sphere has a volume {{nowrap|two-thirds}} that of the circumscribed cylinder and a surface area  {{nowrap|two-thirds}} that of the cylinder (including the bases). Since the values for the cylinder were already known, he obtained, for the first time, the corresponding values for the sphere. The volume of a sphere of radius {{mvar|r}} is {{math|1={{sfrac|4|3}}{{pi}}''r''<sup>3</sup> = {{sfrac|2|3}} (2{{pi}}''r''<sup>3</sup>)}}. The surface area of this sphere is {{math|1=4{{pi}}''r''<sup>2</sup> = {{sfrac|2|3}} (6{{pi}}''r''<sup>2</sup>)}}. A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.