# parts of a ball

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

• Two parallel planes intersecting the ball separate between them from the ball a , which can also be called a spherical frustum (see the frustum).  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 (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

 $A\,=\,2\pi rh.$

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 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