# Sphere

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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 ($V$ ) of a sphere is given by

$\!V={\frac {4\pi r^{3}}{3}}$ where $r$ is the radius of the sphere.

## Surface area

The surface area ($A$ ) of a sphere is given by

$\!A=4\pi r^{2}$ where $r$ is the radius of the sphere.

## Equation of a sphere

In Cartesian coordinates, the equation for a sphere with a center at ($x_{0}$ , $y_{0}$ , $z_{0}$ ) 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.