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Sector of the circle looks like a pizza slice.

The segments are explained in two parts:

As we show in the above diagram a line divides the circle in two parts in which the biggest part of the circle is called the major segment.

Or the lower part or portion is known as a minor segment.

We also calculate the area of segment:

The area of the segment is equal to area of sector minus of area of triangular piece.

\[Area\,\,of\,\,segment = \dfrac{{\left( {\theta - \sin \theta } \right) \times {r^2}}}{2}\,\,\left[ {When\,\,\theta \,\,in\,\,radians} \right]\]

\[Area\,\,of\,\,segment = \left( {\dfrac{{\theta \times \pi }}{{360}} - \dfrac{{\sin \theta }}{2}} \right) \times {r^2}\] (when \[\theta \]is in degrees)

Sector of Circle

The shaded region is the sector of circle.

A sector is created by the central angle formed with two radii and it includes the area inside the circle from that center point to the circle itself. The portion of the circle's circumference bounded by the radii, the arc, is part of the sector.

Common Sectors

The quadrant and semicircle are two special types of sector:

Area of sector\[ = \left( {\dfrac{{\theta ^\circ }}{{360^\circ }}} \right) \times \pi \times {r^2}\]

Where

\[\theta ^\circ \] = degree of the circle

\[R{\text{ }} = {\text{ }}radius{\text{ }}of{\text{ }}the{\text{ }}circle\]