History of the Sphere
Archimedes, (born c. 287 BCE, Syracuse, Sicily [Italy]—died 212/211 BCE, Syracuse), the most famous mathematician and inventor in ancient Greece. Archimedes is especially important for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder. He is known for his formulation of a hydrostatic principle (known as Archimedes’ principle) and a device for raising water, still used, known as the Archimedes screw.
There are nine extant treatises by Archimedes in Greek. The principal results in On the Sphere and Cylinder (in two books) are that the surface area of any sphere of radius r is four times that of its greatest circle (in modern notation, S = 4πr2) 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, V = 4/3πr3). Archimedes was proud enough of the latter discovery to leave instructions for his tomb to be marked with a sphere inscribed in a cylinder. Marcus Tullius Cicero (106–43 BCE) found the tomb, overgrown with vegetation, a century and a half after Archimedes’ death
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sphere with circumscribing cylinder. The volume of a sphere is 4πr3/3, and the volume of the circumscribing cylinder is 2πr3. The surface area of a sphere is 4πr2, and the surface area of the circumscribing cylinder is 6πr2. Hence, any sphere has both two-thirds the volume and two-thirds the surface area of its circumscribing cylinder.
sphere with circumscribing cylinder. The volume of a sphere is 4πr3/3, and the volume of the circumscribing cylinder is 2πr3. The surface area of a sphere is 4πr2, and the surface area of the circumscribing cylinder is 6πr2. Hence, any sphere has both two-thirds the volume and two-thirds the surface area of its circumscribing cylinder.