Area of sector of central angle 200° of a circle is 770 cm². The length of the corresponding arc of this sector is :

1. $70\dfrac{1}{2}$ cm

2. $73\dfrac{1}{3}$ cm

3. 76 cm

4. $80\dfrac{1}{2}$ cm

Given,

Area of sector = 770 cm²

Central angle = 200°

We know that,

$\Rightarrow \text{Area of sector} = \dfrac{\theta}{360°} \times πr^2 \\[1em] \Rightarrow 770 = \dfrac{200°}{360°} \times \dfrac{22}{7} \times r^2 \\[1em] \Rightarrow 35 = \dfrac{5}{9} \times \dfrac{1}{7} \times r^2 \\[1em] \Rightarrow r^2 = 7 \times 9 \times 7 \\[1em] \Rightarrow r^2 = 441 \\[1em] \Rightarrow r = \sqrt{441} \\[1em] \Rightarrow r = 21 \text{ cm}.$

Calculating the arc length :

$\Rightarrow \text{Arc length} = \dfrac{\theta}{360°} \times 2πr \\[1em] = \dfrac{200°}{360°} \times 2 \times \dfrac{22}{7} \times 21 \\[1em] = \dfrac{5}{9} \times 132 \\[1em] = \dfrac{660}{9} \\[1em] = 73\dfrac{1}{3} \text{ cm}.$

Hence, option 2 is the correct option.