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:

Solution:
Area of the sector OAB
$\begin{array}{l}=\frac{1}{2}{r}^2\theta \\ =\frac{1}{2}{\left(10\right)}^2\left(0.354\right)\\ =17.7{\text{ cm}}^2\end{array}$

$\begin{array}{l}=\frac{1}{2}{r}^2\left(\theta -\sin \theta \right)\\ =\frac{1}{2}{\left(6\right)}^2\left(1.333-\sin {1.333}^r\right)\\ =\frac{1}{2}\left(36\right)\left(1.333-0.972\right)\\ =6.498{\text{ cm}}^2\end{array}$