# Sector

## Sector

A portion of space.
In geometry, the term “sector” refers to a portion of two-dimensional or three-dimensional space.

### Properties

• Angular sector
In a plane, a geometric figure defined by the union or the intersection of two half-planes whose boundaries intersect at a point O called the vertex of the angular sector.

• Circular sector
The portion of a circle between two radii.

The area of a circular sector that corresponds to an angle of $$α$$° in a circle of radius $$r$$ has the relationship :
$$A=\dfrac {α} {360}\pi r^{2}$$
• 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 salient, the other re-entrant. The term “spherical sector” usually refers to the salient sector.
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 of a spherical sector that corresponds to a spherical cap of height $$h$$ in a sphere of radius $$r$$ has the relationship :
$$V=\dfrac {2 \pi r^{2} h} {3}$$