Area Of A Sector Of A Circle Formula

Circle

A circle is a geometrical shape which consists of infinitely many points in a plane located at a fixed distance from a point called as the centre of the circle. The fixed distance of any of these points to the centre is called as the radius of the circle.

Arc-

Part of a curve lying on the circumference of a circle.

Length of an arc of a sector- The length of an arc is given as-

Sometimes, the angle of a sector might not be given to you. Instead, the length of the arc is known. In that case, you can calculate the area by using the following.

Sector-

A sector is that part of the circle which is bounded between its two radii and the arc lying between them. Among the sectors of a circle, most usual is a semi-circle which forms half a circle.

A circle with a sector can be subdivided into two areas referred to as a Major Sector and a Minor Sector.

In the figure given below, Since Major represents big or large and Minor represents Small, that's why they are referred to as Major and Minor Sector respectively. No major or minor sector is available in a semi-circle.

We know that a circle measures 360 degrees. Area of a circle is defined as π times the square of its radius length. So if a sector of any circle of radius r measures θ, then the area of the sector can be given by:

Area of sector,

Area of the circular region is πr²

Take this region as a sector making an angle 360° at the centre O.

Now the unitary method for calculating the area of a sector of a circle is to be followed.

When the angle at the centre is 360°, 

area of the sector or the complete circle = πr²

When the angle at the center is 1°, 

area of the sector =

Solved Examples:

Questions1: For a given circle of radius 4 units, the angle of its sector is 45°.Find the area of the sector.

Solution: 

Given, 

radius r = 4 units 

Angle θ = 45° 

Area of the sector = 

=

Questions 2: Find the area of the sector with a central angle of 30° and a radius of 9 cm. 

Solution: 

Given, Radius r = 9 cm 

Angle θ = 30° 

Area of the sector =

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