Sphere
Spherical segment and calotte
If a plane cuts a sphere in two parts, the parts are called spherical segments or segments of the sphere. The volume of the spherical segment is
where r is the radius of sphere and h is the height of spherical segment.
The surface of sphere left is called spherical calotte (like peel of a cut apple). As it is a surface, there is no volume.
where r is the radius of sphere and h is the height of spherical calotte.
![[url=http://materiaalit.internetix.fi/fi/opintojaksot/5luonnontieteet/matematiikka/tietosanakirja/pallo.pdf ]http://materiaalit.internetix.fi/fi/opintojaksot/5luonnontieteet/matematiikka/tietosanakirja/pallo.pdf
[/url]](https://www.geogebra.org/resource/GY3rZsNj/Ggru8W3YqVLZMpJx/material-GY3rZsNj.png)
Frustum of a spherical segment
If a sphere is cut with two horizontal planes, the body between the planes is called frustum of spherical segment.
where are radii of frustum, h is the height of spherical segment.
The surface is called zone of sphere and its area is
where r is the radius of sphere and h is the height of the zone.
Segment of sphere and spherical calotte are special cases of these ones.
Spherical sector
Spherical sector is formed, when the circle of spherical calotte is connected to the centre of sphere. Volume of the spherical sector is
where r is the radius of the sphere and h is the height of the spherical calotte.