Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

Sector

Revision as of 19:39, 24 April 2008 by I like pie (talk | contribs) (Changed wording slightly)
[asy]size(150); real angle1=30, angle2=100; pair O=origin, A=dir(angle2), B=dir(angle1); path sector=O--B--arc(O,1,angle1,angle2)--A--cycle; fill(sector,gray(0.9)); D(unitcircle); D(A--O--B); MP("O",D(O),SSW); MP("A",D(A),NNW); MP("B",D(B),NE); MP("\theta",(0.075,0.075),N);[/asy]

A sector of a circle $O$ is a region bounded by two radii of the circle, $OA$ and $OB$, and the arc $AB$.

Area

The area of a sector $AOB$ is found by multiplying the area of circle $O$ by $\frac{\theta}{2\pi}$, where $\theta=\angle AOB$ is in radians.

Therefore, the area of a sector $AOB$ is $\frac{\theta r^2}{2}$, where $r$ is the radius and $\theta=\angle AOB$ is in radians.

Alternatively, if $\theta$ is in degrees, the area is $\frac{\theta \pi r^2}{360^{\circ}}$.

This article is a stub. Help us out by expanding it.

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=Sector&oldid=25274"