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 r be the radius of the circle.


Given, Central angle = 200° = (200π/180) radians = θ (say)


Thus, Area of the sector = 770 cm2


770 = (1/2)r2θ



= 9 ×49


r = 21 cm


Thus radius of the sector = 21 cm


Now, Length of the corresponding arc = Radius Central angle (in radians)


=


= 220/3 cm = 73.33 cm


Hence, the required length of the corresponding arc is 73.33 cm.


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