Difference between revisions of "Sector"
I like pie (talk | contribs) (Added Asymptote image) |
I like pie (talk | contribs) (Added section Area) |
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MP("O",D(O),SSW); | MP("O",D(O),SSW); | ||
MP("A",D(A),NNW); | MP("A",D(A),NNW); | ||
− | MP("B",D(B),NE);</asy></div> | + | MP("B",D(B),NE); |
+ | MP("\theta",(0.075,0.075),N);</asy></div> | ||
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 == | ||
+ | The [[area]] of a sector <math>AOB</math>, where <math>\theta=\angle AOB</math> is in radians, is found by [[multiply]]ing the area of circle <math>O</math> by <math>\frac{\theta}{2\pi}</math>. | ||
+ | |||
+ | Therefore, the area of a sector <math>AOB</math>, where <math>r</math> is the radius and <math>\theta=\angle AOB</math> is in radians, is <math>\frac{\theta r^2}{2}</math>. | ||
+ | |||
+ | Alternatively, if <math>\theta</math> is in degrees, the area is <math>\frac{\theta \pi r^2}{360^{\circ}}</math>. | ||
{{stub}} | {{stub}} | ||
[[Category:Definition]] | [[Category:Definition]] | ||
[[Category:Geometry]] | [[Category:Geometry]] |
Revision as of 20:37, 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 , where
is in radians, is found by multiplying the area of circle
by
.
Therefore, the area of a sector , where
is the radius and
is in radians, is
.
Alternatively, if is in degrees, the area is
.
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