If a plane cuts a sphere in two parts, the parts are called [color=#0000ff]spherical segments[/color] or segments of the sphere. The volume of the spherical segment is [br][br]  [math]\Large \textcolor{blue}{V=\pi h^2\left ( r-\frac{h}{3}\right)}, [/math][br][br]where [i]r[/i] is the radius of sphere and [i]h[/i] is the height of spherical segment.[br][br]The surface of sphere left is called [color=#0000ff]spherical calotte [/color](like peel of a cut apple). As it is a surface, there is no volume.[br][br]  [math]\large \textcolor{blue}{A=2\pi r h}, [/math][br] [br]where [i]r[/i] is the radius of sphere and [i]h[/i] is the height of spherical calotte.[br][br]

[br]If a sphere is cut with two horizontal planes, the [color=#0000ff]body[/color] between the planes is called [color=#0000ff]frustum of spherical segment[/color].  [br][br]  [math]\Large \textcolor{blue}{V=\frac{1}{2}\pi(r_1^2+r_2^2)h+\frac{1}{6}\pi h^3}[/math][br][br] [br]where [math]r_1^2 \text{ and }r_2^2[/math] are radii of frustum, [i]h[/i] is the height of spherical segment.[br][br][br]The [color=#0000ff]surface[/color] is called [color=#0000ff]zone of sphere[/color] and its area is[br][br]   [math]\large\textcolor{blue}{A=2\pi r h,}[/math][br][br][br]where [i]r[/i] is the radius of sphere and [i]h[/i] is the height of the zone.[br][br][br]Segment of sphere and spherical calotte are special cases of these ones.

Spherical sector is formed, when the circle of spherical calotte is connected to the centre of sphere. Volume of the spherical sector is[br] [br]   [math]\Large \textcolor{blue}{V=\frac{2}{3}\pi r^2h,}[/math][br] [br]where [i]r[/i] is the radius of the sphere and [i]h[/i] is the height of the spherical calotte.[br][br]