A sector of a circle of radius 8 cm contains an angle of $135^o$. Find the area of the sector.

Given:

Radius of the circle $=8\ cm$.

Angle subtended by the sector $=135^o$

To do:

We have to find the area of the sector.

Solution:

Area of the sector subtending $\theta$ at the centre $=\pi r^{2} \times \frac{\theta}{360^{\circ}}$

Therefore,

Area of the given sector $=\pi(8)^{2} \times \frac{135^{\circ}}{360^{\circ}} \mathrm{cm}^{2}$

$=64 \pi \times \frac{3}{8} \mathrm{~cm}^{2}$

$=24\pi \mathrm{cm}^{2}$

The area of the sector is $24\pi \mathrm{cm}^{2}$. 

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Updated on: 10-Oct-2022

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