8.3 Area of a Sector of a Circle

8.3 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.



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


Example 1:

In the above diagram, find the area of the sector OAB.

Solution:
Area of the sector OAB
= 1 2 r 2 θ = 1 2 ( 10 ) 2 ( 0.354 ) = 17.7  cm 2


(B) To Calculate the Area of a Segment of a Circle


Example 2:


The above diagram shows a sector of a circle, with centre Oand a radius 6 cm. The length of the arc ABis 8 cm. Find
(i) Ð AOB
(ii) the area of the shaded segment.

Solution:
(i) Length of the arc AB = 8 cm
                                r θ = 8
                               6 θ = 8
                                  θ = 1.333 radians
Ð AOB = 1.333 radians

(ii) the area of the shaded segment
= 1 2 r 2 ( θ sin θ ) = 1 2 ( 6 ) 2 ( 1.333 sin 1.333 r ) = 1 2 ( 36 ) ( 1.333 0.972 ) = 6.498  cm 2

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