SPHERE

A sphere is a set of all points in three-dimensional Euclidean that are located at a constant distance r from a given center point C. The distance from the center to the sphere is called "radius". Twice the radius is called the diameter d.

The endpoints of any diameter are called antipodes. The equation of a sphere in Euclidean coordinates is given by

x² + y² + z² = r²

The surface S´of a sphere is given by

S = 4 π r²

Its volume V is given by

V = 4π r³ / 3 

The cross section of a sphere is a circle whose radius is maximized if the cutting plane passes through the center of the sphere (note that the cross section degenerates to a point if the the cutting plance becomes a tangent plane).

source: vias