Sphere

round, rotationally symmetric shape of the 2D surface of a ball in 3D space

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.

An image of a sphere

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.

VolumeEdit

The volume ( ) of a sphere is given by

 

where   is the radius of the sphere.

Surface areaEdit

The surface area ( ) of a sphere is given by

 

where   is the radius of the sphere.

Equation of a sphereEdit

In Cartesian coordinates, the equation for a sphere with a center at ( ,  ,  ) is as follows:

 

where   is the radius of the sphere.