Area of a sector of central angle 200° of a circle is 770 cm2. Find the length of the corresponding arc of this sector.
Let the radius of the sector AOBA be r.
Given that, Central angle of sector $A O B A=\theta=200^{\circ}$
and area of the sector $A O B A=770 \mathrm{~cm}^{2}$
We know that, area of the sector $=\frac{\pi r^{2}}{360^{\circ}} \times \theta^{\circ}$
$\therefore \quad$ Area of the sector, $770=\frac{\pi r^{2}}{360^{\circ}} \times 200$
$\Rightarrow \quad \frac{77 \times 18}{\pi}=r^{2}$
$\Rightarrow \quad r^{2}=\frac{77 \times 18}{22} \times 7 \Rightarrow r^{2}=9 \times 49$
$\Rightarrow \quad r=3 \times 7$
$\therefore \quad r=21 \mathrm{~cm}$
So, radius of the sector $A O B A=21 \mathrm{~cm}$.
Now, the length of the correspoding arc of this sector $=$ Central angle $\times$ Radius
$=200 \times 21 \times \frac{\pi}{180^{\circ}} \quad\left[\because 1^{\circ}=\frac{\pi}{180} R\right]$
$=\frac{20}{18} \times 21 \times \frac{22}{7}$
$=\frac{220}{3} \mathrm{~cm}=73 \frac{1}{3} \mathrm{~cm}$
Hence, the required length of the corresponding arc is $73 \frac{1}{3} \mathrm{~cm}$.
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