parts of a ball

Let us consider in 3 a ball of radius r and the sphere bounding the ball.

  • Two parallel planesMathworldPlanetmath intersecting the ball separate between them from the ball a spherical segmentMathworldPlanetmath, which can also be called a spherical frustum (see the frustumMathworldPlanetmath).  The curved surface of the spherical segment is the spherical zone.

  • In the special case that one of the planes is a tangent plane of the sphere, the spherical segment is a spherical cap and the spherical zone is a spherical calotte.

  • The lateral surface of a circular cone with its apex in the centre ( of the ball divides the ball into two spherical sectors.

The distanceMathworldPlanetmath h of the two planes intersecting the ball be is called the height.

The volume of the spherical cap is obtained from


and the area of the corresponding spherical calotte and also a spherical zone from

A= 2πrh.

The volume of a spherical segment can be got as the difference of the volumes of two spherical caps.

The volume of a spherical sector may be calculated from


where h is the height of the spherical cap of the spherical sector.

Title parts of a ball
Canonical name PartsOfABall
Date of creation 2013-03-22 18:18:36
Last modified on 2013-03-22 18:18:36
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 10
Author pahio (2872)
Entry type Definition
Classification msc 51M05
Synonym parts of ball
Synonym parts of sphere
Related topic CircularSegment
Defines spherical segment
Defines spherical frustum
Defines spherical cap
Defines spherical calotte
Defines spherical sector