Question:
A sector of a circle of radius 8 cm contains an angle of 135°. Find the area of the sector.
Solution:
We know that the area A of a sector of an angle θ in the circle of radius r is given by
$A=\frac{\theta}{360^{\circ}} \times \pi r^{2}$
It is given that $r=8 \mathrm{~cm}$ and $\theta=135^{\circ}$.
Now we substitute the value of $r$ and $\theta$ in above formula,
$A=\frac{135^{\circ}}{360^{\circ}} \times \pi \times 8 \times 8 \mathrm{~cm}^{2}$
$=24 \pi \mathrm{cm}^{2}$
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