Circular sector

A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the minor sector and the larger being the major sector. In the diagram, is the central angle, the radius of the circle, and is the arc length of the minor sector.

A circular sector, also known as circle sector or disk sector or simply a sector (symbol: ⌔), is the portion of a disk (a closed region bounded by a circle) enclosed by two radii and an arc, with the smaller area being known as the minor sector and the larger being the major sector. In the diagram, is the central angle, the radius of the circle, and is the arc length of the minor sector. A = \pi r^2\, \frac{L}{2\pi r} = \frac{rL}{2} The area of the sector can be obtained by multiplying the circle's area by the ratio of the angle (expressed in radians) and (because the area of the sector is directly proportional to its angle, and is the angle for the whole circle, in radians): A = \pi r^2\, \frac{\theta}{2 \pi} = \frac{r^2 \theta}{2} Another approach is to consider this area as the result of the following integral: A = \int_0^\theta\int_0^r dA = \int_0^\theta\int_0^r \tilde{r}\, d\tilde{r}\, d\tilde{\theta} = \int_0^\theta \frac 1 2 r^2\, d\tilde{\theta} = \frac{r^2 \theta}{2} Converting the central angle into degrees gives A = \pi r^2 \frac{\theta^\circ}{360^\circ} L = r \theta where represents the arc length, represents the radius of the circle and represents the angle in radians made by the arc at the centre of the circle. If the value of angle is given in degrees, then we can also use the following formula by: L = 2 \pi r \frac{\theta}{360^\circ} P = L + 2r = \theta r + 2r = r (\theta + 2) where is in radians. C = 2r\sin\frac{\theta}{2} where represents the chord length, represents the radius of the circle, and represents the angular width of the sector in radians.

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