sector of a circle∗
CWoo†
2013-03-21 15:07:30
A sector is a fraction of the interior of a circle, described by a central angle
θ. If θ = 2π, the sector becomes a complete circle.
If the central angle is θ, and the radius of the circle is r, then the area of the
sector is given by
1 2
r θ
2
θ
This is obvious from the fact that the area of a sector is 2π
times the area
2
of the circle (which is πr ). Note that, in the formula, θ is in radians.
Remark. Since the length a of the arc of the sector is rθ, the area of the
sector is 21 ar, which is equal to the area of a triangle with base = a and the
height = r.
∗ hSectorOfACirclei created: h2013-03-21i by: hCWooi version: h33617i Privacy setting:
h1i hDefinitioni h51-00i
† This text is available under the Creative Commons Attribution/Share-Alike License 3.0.
You can reuse this document or portions thereof only if you do so under terms that are
compatible with the CC-BY-SA license.
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