archimedes discovered the formulas for the surface area and volume of a sphere.
archimedes discovered the formulas for the surface area and volume of a sphere.
who discovered the formulas for the surface area and volume of a sphere?
archimedes
in the treatise by this name, written c. 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 circumscribed right circular cylinder of the same height and diameter. the sphere has a volume that of the circumscribed cylinder and a surface area 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 is . the surface area of this sphere is . a sculpted sphere and cylinder were placed on the tomb of archimedes at his request.
cylinder
spheres for are sometimes called hyperspheres.









































the -sphere of unit radius centered at the origin is denoted and is often referred to as "the" -sphere. note that the ordinary sphere is a 2-sphere, because it is a 2-dimensional surface (which is embedded in 3-dimensional space).









































the surface area of the unit ()-sphere is









































where is euler's gamma function.









































another expression for the surface area is









































and the volume is the surface area times or









































general recursive formulas also exist for the volume of an -ball.









































section::::generalizations.:metric spaces.
sphere