Find the area of the sector of a circle

Question:

Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Solution:

Let the central angle of the sector be θ.

Given that, radius of the sector of a circle (r) = 5 cm.

and arc length $(l)=3.5 \mathrm{~cm}$

$\therefore$ Central angle of the sector, $\theta=\frac{\operatorname{arc} \text { length }(l)}{\text { radius }}$

 $\left[\because \theta=\frac{l}{r}\right]$$\Rightarrow$ $\theta=\frac{3.5}{5}=0.7 R$

$\Rightarrow$ $\theta=\left(0.7 \times \frac{180}{\pi}\right)^{\circ}\left[\because 1 R=\frac{180^{\circ}}{\pi} D^{\circ}\right]$

Now orna of eneter with angla $A-07$

$=\frac{\pi r^{2}}{360^{\circ}} \times(0.7) \times \frac{180^{\circ}}{\pi}$

$=\frac{(5)^{2}}{2} \times 0.7=\frac{25 \times 7}{2 \times 10}=\frac{175}{20}=8.75 \mathrm{~cm}^{2}$

Hence, required area of the sector of a circle is $8.75 \mathrm{~cm}^{2}$

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