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

Sum

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 = (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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#### APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 11 Area Related To Circles
Exercise 11.4 | Q 15 | Page 134
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