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.

Answer 1

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"`.