Difference between revisions of "Sector"
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== Area == | == Area == | ||
− | The [[area]] of a sector <math>AOB</math> is found by [[multiply]]ing the area of circle <math>O</math> by <math>\frac{\theta}{2\pi}</math>, where <math>\theta | + | The [[area]] of a sector <math>AOB</math> 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, <math>\angle AOB</math>, in radians. |
− | Therefore, the area of a sector <math>AOB</math> is <math>\frac{ | + | Therefore, the area of a sector <math>AOB</math> is <math>\frac{r^2\theta}{2}</math>, where <math>r</math> is the radius and <math>\theta=\angle AOB</math> is in radians. |
− | Alternatively, if <math>\theta</math> is in degrees, the area is <math>\frac{ | + | Alternatively, if <math>\theta</math> is in degrees, the area is <math>\frac{\pi r^2\theta}{360^{\circ}}</math>. |
{{stub}} | {{stub}} | ||
[[Category:Definition]] | [[Category:Definition]] | ||
[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 20:49, 24 April 2008
![[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]](http://latex.artofproblemsolving.com/3/0/3/303f796fa9c544e25a8eab2c1c9de9508c532b8f.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 in radians.
Alternatively, if is in degrees, the area is
.
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