8.3 Area of a Sector of a Circle
(A) Area of a Sector of a Circle
(A) Area of a Sector of a Circle
1. If a circle divided into two sectors of different sizes, the smaller sector is known as the minor sector while the larger sector is known as the major sector.
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2013/11/Picture8.png)
2. If AOB is the area of a sector of a circle, of radius r, that subtends an angle θ radians, at the centre O, then
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2013/11/Picture7.png)
Example 1:
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2013/11/Picture11-300x288.png)
In the above diagram, find the area of the sector OAB.
Solution:
Area of the sector OAB
(B) To Calculate the Area of a Segment of a Circle
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2013/11/Picture9.png)
Example 2:
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2013/11/Picture10-1.png)
![](http://spmaddmaths.blog.onlinetuition.com.my/wp-content/uploads/sites/3/2013/11/Picture10-1.png)
The above diagram shows a sector of a circle, with centre O and a radius 6 cm. The length of the arc AB is 8 cm. Find
(i) ∠AOB
(ii) the area of the shaded segment.
Solution:
(i) Length of the arc AB = 8 cm
rθ = 8
6θ = 8
θ = 1.333 radians
∠AOB = 1.333 radians
(ii)
the area of the shaded segment
the area of the shaded segment