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Sum

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.

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#### 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 cm^{2}

We know that, area of the sector = `(pir^2)/360^circ xx theta^circ`

⇒ `(77 xx 18)/pi = r^2`

⇒ `r^2 = (77 xx 18)/22 xx 7`

⇒ `r^2 = 9 xx 49`

⇒ `r = 3 xx 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 .....`[because theta = l/r]`

= `200 xx 21 xx pi/180^circ` ....`[because 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.

Concept: Areas of Sector and Segment of a Circle

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