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

Question

Area of a sector of central angle 200° of a circle is 770 cm 2 . Find the length of the corresponding arc of this sector.

Philoid · Accepted Answer

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.