Question

Question 8
Find the area of the sector of a circle of radius 5 cm, if the corresponding arc length is 3.5 cm.

Answer 1

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

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

And arc length (l) =3.5 cm

$\therefore$ Central angle of the sector $=\theta =\frac{arclength\left(l\right)}{radius}$

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

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

Now, area of sector with angle $\theta =0.7$

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

$=\frac{(5{)}^2}{2}\times 0.7=\frac{25\times 7}{2\times 10}=\frac{175}{20}=8.75c{m}^2$

Hence, the required area of the sector of a circle is $8.75c{m}^2$