Difference between revisions of "Sector"
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A '''sector''' of a [[circle]] <math>O</math> is a region bounded by two [[radius|radii]] of the circle, <math>OA</math> and <math>OB</math>, and the [[arc]] <math>AB</math>. | A '''sector''' of a [[circle]] <math>O</math> is a region bounded by two [[radius|radii]] of the circle, <math>OA</math> and <math>OB</math>, and the [[arc]] <math>AB</math>. | ||
| − | == Area == | + | ==Area== |
The [[area]] of a sector is found by [[multiply]]ing the area of circle <math>O</math> by <math>\frac{\theta}{2\pi}</math>, where <math>\theta</math> is the [[central angle]] in radians. | The [[area]] of a sector is found by [[multiply]]ing the area of circle <math>O</math> by <math>\frac{\theta}{2\pi}</math>, where <math>\theta</math> is the [[central angle]] in radians. | ||
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Alternatively, if <math>\theta</math> is in degrees, the area is <math>\frac{\pi r^2\theta}{360^{\circ}}</math>. | Alternatively, if <math>\theta</math> is in degrees, the area is <math>\frac{\pi r^2\theta}{360^{\circ}}</math>. | ||
| + | |||
| + | ==See also== | ||
| + | *[[Semicircle]] | ||
{{stub}} | {{stub}} | ||
[[Category:Definition]] | [[Category:Definition]] | ||
[[Category:Geometry]] | [[Category:Geometry]] | ||
Revision as of 19:58, 24 April 2008
![[asy]size(150); real angle1=30, angle2=120; 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),NW); MP("B",D(B),NE); MP("\theta",(0.05,0.075),N);[/asy]](http://latex.artofproblemsolving.com/7/c/9/7c9a7756f90fe421d7f60125f66669fa9200d25d.png)
A sector of a circle 
is a region bounded by two radii of the circle, 
and 
, and the arc 
.
Area
The area of a sector is found by multiplying the area of circle by 
, where 
is the central angle in radians.
Therefore, the area of a sector is 
, where 
is the radius and is the central angle in radians.
Alternatively, if is in degrees, the area is 
.
See also
This article is a stub. Help us out by expanding it.
