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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 spherical segment, 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 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.
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