Sphere

An image of a sphere

A sphere is a shape in space that is like the surface of a ball. Most of the time, the terms ball and sphere are used as the same. But in mathematics, the precise (exact) definition only allows points in the 3 dimensional space which are uniformly and symmetrically located at a fixed length called radius of the sphere.

Examples of these are basketballs, superballs, and playground balls.

A sphere is the 3 dimensional analogue of a circle.

Volume

The volume (V) of a sphere is given by the following formula

$\!V={\frac {4}{3}}\pi r^{3}$

where r is the radius of the sphere.

Surface area

The surface area (A) of a sphere is given by the following formula

$\!A=4\pi r^{2}$

where r is the radius of the sphere.

Equation of a sphere

In Cartesian co-ordinates, the equation for a sphere with a center at (x₀, y₀, z₀) is as follows:

$(x-x_{0})^{2}+(y-y_{0})^{2}+(z-z_{0})^{2}=r^{2}$

where r is the radius of the sphere.