On the Sphere and Cylinder

On the Sphere and Cylinder is a work that was published by Archimedes in two volumes c. 225 BCE. It most notably details how to find the surface area of a sphere and the volume of the contained ball and the analogous values for a cylinder, and was the first to do so. Contents The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder. Let be the radius of the sphere and cylinder, and be the height of the cylinder, with the assumption that the cylinder is a right cylinder—the side is perpendicular to both caps. In his work, Archimedes showed that the surface area of a cylinder is equal to: and that the volume of the same is: