# 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 $=r$.

Title | sector of a circle |
---|---|

Canonical name | SectorOfACircle |

Date of creation | 2013-03-22 13:10:20 |

Last modified on | 2013-03-22 13:10:20 |

Owner | CWoo (3771) |

Last modified by | CWoo (3771) |

Numerical id | 6 |

Author | CWoo (3771) |

Entry type | Definition |

Classification | msc 51-00 |

Synonym | sector |