Sphere

(Redirected from Orb)
An image of a sphere

A sphere is a shape in space that is like the surface of a ball. Usually, the words ball and sphere mean the same thing. But in mathematics, a sphere is the surface of a ball, which is given by all the points in three dimensional space that are located at a fixed distance from the center. The distance from the center is called radius of the sphere. When the sphere is filled in with all the points inside, it called a ball.

Common things that have the shape of a sphere are are basketballs, superballs, and playground balls. The Earth and the Sun are nearly spherical, meaning sphere-shaped.

A sphere is the three-dimensional analog of a circle.

Volume

The volume (${\displaystyle V}$) of a sphere is given by

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

where ${\displaystyle r}$ is the radius of the sphere.

Surface area

The surface area (${\displaystyle A}$) of a sphere is given by

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

where ${\displaystyle r}$ is the radius of the sphere.

Equation of a sphere

In Cartesian coordinates, the equation for a sphere with a center at (${\displaystyle x_{0}}$, ${\displaystyle y_{0}}$, ${\displaystyle z_{0}}$) is as follows:

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

where ${\displaystyle r}$ is the radius of the sphere.