parts of a ball
Let us consider in ${\mathbb{R}}^{3}$ a ball of radius $r$ and the sphere bounding the ball.

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Two parallel planes^{} intersecting the ball separate between them from the ball a spherical segment^{}, which can also be called a spherical frustum (see the frustum^{}). The curved surface of the spherical segment is the spherical zone.

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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.

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The lateral surface of a circular cone with its apex in the centre (http://planetmath.org/Sphere) of the ball divides the ball into two spherical sectors.
The distance^{} $h$ of the two planes intersecting the ball be is called the height.
The volume of the spherical cap is obtained from
$$V=\pi {h}^{2}\left(r\frac{h}{3}\right)$$ 
and the area of the corresponding spherical calotte and also a spherical zone from
$$A=\mathrm{\hspace{0.17em}2}\pi rh.$$ 
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
$$V=\frac{2}{3}\pi {r}^{2}h,$$ 
where $h$ is the height of the spherical cap of the spherical sector.
Title  parts of a ball 
Canonical name  PartsOfABall 
Date of creation  20130322 18:18:36 
Last modified on  20130322 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 