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
where r is the radius of the sphere.
Surface area
The surface area (A) of a sphere is given by the following formula
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:
where r is the radius of the sphere.
Images for kids

r â€“ radius of the sphere

An image of one of the most accurate humanmade spheres, as it refracts the image of Einstein in the background. This sphere was a fused quartz gyroscope for the Gravity Probe B experiment, and differs in shape from a perfect sphere by no more than 40 atoms (less than 10 nanometers) of thickness. It was announced on 1 July 2008 that Australian scientists had created even more nearly perfect spheres, accurate to 0.3Â nanometers, as part of an international hunt to find a new global standard kilogram.

Great circle on a sphere

A normal vector to a sphere, a normal plane and its normal section. The curvature of the curve of intersection is the sectional curvature. For the sphere each normal section through a given point will be a circle of the same radius, the radius of the sphere. This means that every point on the sphere will be an umbilical point.