PlanetMath: sector of a circle

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sector of a circle

(Definition)

A sector is a fraction of the interior of a circle, described by a central angle $\theta$ . If $\theta = 2 \pi,$ the sector becomes a complete circle.

$\includegraphics{sector.eps}$

If the central angle is $\theta,$ and the radius of the circle is then the area of the sector is given by

$\displaystyle Area = \frac{1}{2}r^2\theta$

This is obvious from the fact that the area of a sector is $\frac{\theta}{2 \pi}$ times the area of the circle (which is $\pi r^2$ ). Note that, in the formula, $\theta$ is in radians.

Remark. Since the length of the arc of the sector is $r\theta$ , the area of the sector is $\frac{1}{2}ar$ , which is equal to the area of a triangle with base and the height .

"sector of a circle" is owned by CWoo. [ full author list (2) | owner history (1) ]

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sector

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Cross-references: height, base, area of a triangle, arc, length, radians, obvious, area, radius, central angle, circle, fraction
There are 6 references to this entry.

This is version 2 of sector of a circle, born on 2002-11-23, modified 2007-11-27.
Object id is 3617, canonical name is SectorOfACircle.
Accessed 14349 times total.

Classification:

AMS MSC:

51-00 (Geometry :: General reference works )

Pending Errata and Addenda

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