Find the area of the sector of a circle of radius $ 5 \mathrm{~cm} $, if the corresponding arc length is $ 3.5 \mathrm{~cm} $.

Given:

Radius of the circle $r=5 \mathrm{~cm}$.

Length of the corresponding arc $=3.5 \mathrm{cm}$

To do:

We have to find the area of the sector.

Solution:

Let the central angle of the sector be $\theta$.

Central angle of the sector $\theta=\frac{Arc\ length}{Radius}$

$=\frac{3.5}{5}$

$=0.7\ R$

$=(0.7\times\frac{180}{\pi})^o$

Area of the sector $=\pi r^2 \frac{\theta}{360^o}$

$=\pi 5^2 \times (0.7\times\frac{180}{\pi})^o \times \frac{1}{360^o}$

$=25\times0.7 \times \frac{1}{2}$

$=8.75\ cm^2$

The area of the sector is $8.75\ cm^2$.

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Updated on: 10-Oct-2022

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