Best Way to Learn Area of Sector Formula in Details with Solved Examples
In this session, you will learn what a sector of a circle is and how to calculate a sector's area.
What is the Area of a Sector?
The area of a sector is the measure of space occupied by a sector of a circle. A circle's sector always originates from the circle's centre. A sector is a part of the circle covered by 2 radii and an arc, such as a pizza slice. If we divide a circle into 6 equal parts like a pizza slice, then all of them are the sectors of this circle.
The area of a sector helps to find the area of a part of a circle regardless of how big or small the part is. There are two types of sectors: minor and major sectors. The minor sector is a sector that is less than a semi-circle, whereas the major sector is a sector greater than a semi-circle.
Area of Sector Formula
If a sector of circle makes an angle θ with the centre and the radius of the circle is r then the sector of a circle formula is:
Where θ is the angle made by the sector of a circle in radian and r is the radius of the circle.
So these are two different formulas to calculate area of a sector.
Derivation of Area of a Sector Formula
As we already learnt the area of a circle formula, that is:
$$ A \;=\; \pi r^2 $$If we divide the circle in 4 parts, then all four parts of the circle are the sector of the circle. To find the area of sector, we will divide total area of the circle by 4 as:
$$ A \;=\; \frac{1}{4} \pi r^2 $$Now, since we know that the total measure of a circle is 360 degrees, the area of the circle will be,
$$ A \;=\; \frac{1}{360} \pi r^2 $$If the central angle is then, the area of sector of circle formula will be:
$$ A \;=\; \frac{θ}{360} \pi r^2 $$How to Find Sector Area?
The area of a sector can be calculated by using following area of arc formula:
- When the angle made by the sector is in degrees: $$ A \;=\; \frac{θ}{360} \pi r^2 $$
- When the angle made by the sector is in radian: $$ A \;=\; \frac{θ}{2} \pi r^2 $$
Let’s see the following example to understand how to calculate area of sector.
FAQ’s
What is a Sector Area in Maths?
The sector area is the total space occupied by the part of a circle. It the measure of a small portion within a circle.
What is the Sector Area Formula?
If a sector of circle makes an angle θ with the centre and the radius of the circle is r then the formula of sector of a circle is:
$$ A \;=\; \frac{\theta}{360} \pi r^2 $$Is the Sector the same as Arc Length?
No, the sector and the arc length are different from each other. The arc length is the measure of a curved part of the circle and the sector area is the area of a part of a circle.
