Spherical Sector
If the radius of a sphere revolves around the boundary of a small circle of the sphere, it forms a conical surface and divides the sphere into two spherical sectors, one minor, the other major.
The term "spherical sector" usually refers to the salient sector, or the sector that is convex. This sector can be described as the union of a spherical cap and a cone whose vertex is at the centre of the sphere and whose base corresponds to the base of the spherical cap.
The volume V of a spherical sector that corresponds to a spherical cap of height h in a sphere of radius r is given by the relationship:
The volume V of a spherical sector that corresponds to a spherical cap of height h in a sphere of radius r is given by the relationship:
[latex]V=\dfrac {2 \pi r^{2} h} {3}[/latex]
The total area A of a spherical sector of radius R and height h in a sphere of radius r is given by the formula:[latex]A=2\pi rh+\pi Rr=\pi r\left ( 2h+R \right )[/latex]