# Area Of A Sector Of A Circle Formula

## Area Of A Sector Of A Circle Formula

A sector is a portion of a circle defined by the arc connecting its two radii. The most common sector of a circle is a semicircle, which represents half of a circle. An arc and its two radii form a pie-shaped portion of a circle known as a sector. When two radii and a portion of the circle’s circumference—also referred to as an arc—meet at the arc’s two extremities, the result is a sector. The region inside a sector of a circle’s border is referred to as the Area Of A Sector Of A Circle Formula. The centre of the circle marks the start of each sector. In this instance, a circle has two sectors of equal size, one of which is the semicircle.

The Area Of A Sector Of A Circle Formula is

A = (θ/360) πr2

where

θ is the sector angle that the arcs at the centre subtend (in degrees).

The circle’s radius is denoted by r.

The area is determined by A = ½* r2 *r

where r is the subtended angle in radians.

## Circle-

A circle is a geometric figure that is composed of an unlimited number of points in a plane that are spaced uniformly apart from the point that is known as the circle’s centre. The radius of the circle is the set distance between any of these points and the centre. A circle can also be described as a particular type of ellipse where the semi-major and semi-minor axes are equal, the eccentricity is 0, and the two foci are coincident, or as the two-dimensional shape with the greatest area per unit, perimeter squared when applying the calculus of variations.

## Arc-

An arc is a section of a curve that lies on a circle’s circumference.  There are times when one might not be given the sector’s aspect. Instead, the arc’s length is known. In these situations, one can use the formulas to calculate the Area Of A Sector Of A Circle Formula.

## Sector-

The part of a circle that is contained within its two radii and the arc that connects them is called a sector. A semicircle, which represents one-half of a circle, is the most frequent sector of a circle. Two more regions, known as a Major Sector and a Minor Sector, can be created within a circle that contains a sector. Since Major and Minor signify big and small, respectively, they are referred to as the Major and Minor Sectors. There are no major or minor sectors in a semicircle. It is known that a whole circle has 360 degrees in it. The formula for calculating a circle’s area is π times the radius’s square.

### Area of a Sector

Area Of A Sector Of A Circle Formula is

A = (θ/360) πr2

### Derivation

With the formula for the area of a circle known, the Area Of A Sector Of A Circle Formula can be calculated. If the circle is divided into four pieces, each of those four pieces constitutes a circle sector. One shall divide the circle’s overall area by four to determine the Area Of A Sector Of A Circle Formula. Now that it is known that a circle has a circumference of 360 degrees, one can calculate the circle’s area. The formula for the Area Of A Sector Of A Circle Formula can then be calculated.

### Sample Problems

Sample problems on the Area Of A Sector Of A Circle Formula can be found on the Extramarks website and mobile application. These problems are crucial to understanding the concept of the Area Of A Sector Of A Circle Formula.