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.

Options

A. `73(1)/(3)` cm
B. `73(1)/(2)` cm
C. `72(1)/(3)` cm
D. `72(1)/(2)` cm

Explanation

Let the radius of the sector AOBA be r.
Given that, central angle of sector `AOBA = theta= 200^(@)`
and area of the sector AOBA = `770cm^(2)`
we know that, area of the sector = `(pir^(2))/(360^(@))xxtheta^(@)`
`:.` Area of the sector, `770 = (pir^(2))/(360^(@))xx200`
`rArr (77xx18)/(pi)=r^(2)`
`rArr r^(2) = (77xx 18)/(22)xx7 rArr r^(2) = 9xx 49`
`rArr r = 3xx7`
`:.` r = 21 cm
So, radius of the sector AOBA = 21 cm.
Now, the length of the correspoding arc of this sector= Central `xx` Radius [`because theta= (l)/(r)`]
= ` 200 xx 21 xx (pi)/(180^(@))` [`because 1^(@) = (pi)/(180)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` .