He discovered the relationship between a sphere and a circumscribed cylinder of the same height and diameter. The volume is 4â„3Ï€r3 for the sphere, and 2Ï€r3 for the cylinder. The surface area is 4Ï€r2 for the sphere, and 6Ï€r2 for the cylinder (including its two bases), where r is the radius of the sphere and cylinder. The sphere has a volume and surface area two-thirds that of the cylinder. A sculpted sphere and cylinder were placed on the tomb of Archimedes at his request.