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A wireframe sphere.

A sphere is the set of all points in three-dimensional euclidean space (R3) which are at a fixed distance r (called radius) away from a point called the center.

A generalization of it is the set of points which in some vector space is, according to a specified norm, equidistant.

The surface area of a sphere is equal to four times pi times the square of the radius, and the volume of a sphere is equal to four-thirds times the cube of the radius. Thus:

  • SA=4πr²
  • V=1⅓πr³

For any positive radius r.