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Question
Area of a sector of central angle 200° of a circle is 770 cm2. Find the length of the corresponding arc of this sector.
Solution
Let the radius of the sector AOBA be r.
Given that, Central angle of sector AOBA = θ = 200°
And area of the sector AOBA = 770 cm2
We know that, area of the sector = `(pi"r"^2)/360^circ xx θ^circ`
∴ Area of the sector, 770 = `(pi"r"^2)/360^circ xx 200`
⇒ `(77 xx 18)/pi` = r2
⇒ r2 = `(77 xx 18)/22 xx 7`
⇒ r2 = 9 × 49
⇒ r = 3 × 7
∴ r = 21 cm
So, radius of the sector AOBA = 21 cm.
Now, the length of the corresponding arc of this sector = Central angle × Radius ...`[∵ θ = l/"r"]`
= `200 xx 21 xx pi/180^circ` ...`[∵ 1^circ = pi/180^circ "R"]`
= `20/18 xx 21 xx 22/7`
= `220/3 "cm"`
= `73 1/3 "cm"`
Hence, the required length of the corresponding arc is `73 1/3 "cm"`.
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