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Circular sector: Wikis

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Categories: Circles

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Updated live from Wikipedia, last check: May 31, 2012 14:11 UTC (54 seconds ago)

From Wikipedia, the free encyclopedia

A circular sector is shaded in green

A circular sector or circle sector, is the portion of a circle enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector. Its area can be calculated as described below.

Let θ be the central angle, in radians, and $r$ the radius. The total area of a circle is $π r 2$ . The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle and $2π$ (because the area of the sector is proportional to the angle, and $2π$ is the angle for the whole circle):

$A = \pi r^2 \cdot \frac{\theta}{2 \pi} = r^2 \left( \frac{\theta}{2} \right) = \frac{1}{2} r^2 \theta.$

Also, if $θ$ refers to the central angle in degrees, a similar formula can be derived.

$A = \pi r^2 \cdot \frac{\theta}{360}$

Sectors can have special relationships, which include halves, quadrants, and octants.

The length, $L$ , of the arc of a sector is given by the following formula:

$L = \left( \pi \cdot r \cdot \frac{\theta}{180}\right)$

where θ is in degrees.

The length of the perimeter of a sector is sum of arc length and the two radii. It is given by the following formula:

$L = r \cdot \left( 2 + \pi \cdot \frac{\theta}{180}\right)$

where θ is in degrees.

The angle formed by connecting the endpoints of the sector to any point on the circle that is not in that sector is equal to half the arc length.

See also

Circular segment - the part of the sector which remains after removing the triangle formed by the center of the circle and the two endpoints of the circular arc on the boundary.
Conic section

External links

Definition and properties of a circle sector With interactive animation
Wolfram MathWorld: Circular Sector

Categories: Circles | Geometry stubs

Related links

Up to date as of November 16, 2009

This page is marked authoritative because it has been included for <B>86%</B> of the life of the Wikipedia article.

Definition and properties of a circle sector - Sector definition - Math Open Reference

Wolfram MathWorld: Circular Sector - Circular Sector -- from Wolfram MathWorld

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