sector of a circle

A sector is a fraction of the interior of a circle, described by a central angleMathworldPlanetmath θ. If θ=2π, the sector becomes a completePlanetmathPlanetmath circle.

If the central angle is θ, and the radius of the circle is r, then the area of the sector is given by


This is obvious from the fact that the area of a sector is θ2π times the area of the circle (which is πr2). Note that, in the formula, θ is in radians.

Remark. Since the length a of the arc of the sector is rθ, the area of the sector is 12ar, which is equal to the area of a triangle with base =a and the height =r.

Title sector of a circle
Canonical name SectorOfACircle
Date of creation 2013-03-22 13:10:20
Last modified on 2013-03-22 13:10:20
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 6
Author CWoo (3771)
Entry type Definition
Classification msc 51-00
Synonym sector