[size=150]Archimedes, (born c. 287 BCE, Syracuse, [url=https://www.britannica.com/place/Sicily]Sicily[/url] [Italy]—died 212/211 BCE, Syracuse), the most famous mathematician and inventor in [url=https://www.britannica.com/place/ancient-Greece]ancient Greece[/url]. Archimedes is especially important for his discovery of the relation between the [url=https://www.britannica.com/science/surface-geometry]surface[/url] and volume of a sphere and its circumscribing [url=https://www.britannica.com/science/cylinder-mathematics]cylinder[/url]. He is known for his formulation of a [url=https://www.britannica.com/science/hydrostatics]hydrostatic[/url] principle (known as [url=https://www.britannica.com/science/Archimedes-principle]Archimedes’ principle[/url]) and a device for raising water, still used, known as the [url=https://www.britannica.com/technology/Archimedes-screw]Archimedes screw[/url].[br][br]There are nine [url=https://www.merriam-webster.com/dictionary/extant]extant[/url] [url=https://www.merriam-webster.com/dictionary/treatises]treatises[/url] by Archimedes in Greek. The principal results in [i]On the Sphere and Cylinder[/i] (in two books) are that the surface area of any [url=https://www.britannica.com/science/sphere]sphere[/url] of radius [i]r[/i] is four times that of its greatest [url=https://www.britannica.com/science/circle-mathematics]circle[/url] (in modern notation, [i]S[/i] = 4π[i]r[/i][sup]2[/sup]) and that the volume of a sphere is two-thirds that of the cylinder in which it is inscribed (leading immediately to the formula for the volume, [i]V[/i] = [sup]4[/sup]/[sub]3[/sub]π[i]r[/i][sup]3[/sup]). Archimedes was proud enough of the latter discovery to leave instructions for his tomb to be marked with a sphere inscribed in a cylinder. [url=https://www.britannica.com/biography/Cicero]Marcus Tullius Cicero[/url] (106–43 BCE) found the tomb, overgrown with vegetation, a century and a half after Archimedes’ death[/size][size=100][br][br][br].[/size][url=https://cdn.britannica.com/11/66811-004-E4CCA736/circumscribing-cylinder-Sphere-volume-sphere-surface-area.jpg][img]https://cdn.britannica.com/s:690x388,c:crop/11/66811-004-E4CCA736/circumscribing-cylinder-Sphere-volume-sphere-surface-area.jpg[/img][br][br][br][/url][size=100][size=150][url=https://cdn.britannica.com/11/66811-004-E4CCA736/circumscribing-cylinder-Sphere-volume-sphere-surface-area.jpg]s[/url][url=https://cdn.britannica.com/11/66811-004-E4CCA736/circumscribing-cylinder-Sphere-volume-sphere-surface-area.jpg]phere with circumscribing [/url]cylinder. The volume of a sphere is 4π[i]r[/i][sup]3[/sup]/3, and the volume of the circumscribing cylinder is 2π[i]r[/i][sup]3[/sup]. The surface area of a sphere is 4π[i]r[/i][sup]2[/sup], and the surface area of the circumscribing cylinder is 6π[i]r[/i][sup]2[/sup]. Hence, any sphere has both two-thirds the volume and two-thirds the surface area of its circumscribing cylinder.[/size][/size]