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Homesector of a circle

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# sector of a circle

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.

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

$\frac{1}{2}r^{2}\theta$ |

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 $=r$.

Synonym:

sector

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

51-00*no label found*

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