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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 $ r,$ 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 $ a$ 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 $ =a$ and the height $ =r$.



"sector of a circle" is owned by CWoo. [ full author list (2) | owner history (1) ]
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Other names:  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 MSC51-00 (Geometry :: General reference works )

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