A sphere (from Greek — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point. This distance r is known as the radius of the sphere. The maximum straight distance through the sphere is known as the diameter of the sphere. It passes through the center and is thus twice the radius.

In higher mathematics, a careful distinction is made between the surface of a sphere (referred to as a “sphere”), and the inside of a sphere (referred to as a “ball”). Thus, a sphere in three dimensions is considered to be a two-dimensional spherical surface embedded in three-dimensional Euclidean space, while a ball is a solid figure bounded by a sphere.

This article deals with the mathematical concept of a sphere. In physics, a sphere is an object (usually idealized for the sake of simplicity) capable of colliding or stacking with other objects which occupy space.

Volume

In 3 dimensions, the volume inside a sphere is given by the formula

where r is the radius of the sphere, d = 2r is the diameter of the sphere and π is the constant pi.

 Surface area of a sphere

The surface area of a sphere is given by the formula