Question

A circle of radius 120 m is divided into 8 equal sectors. Find the length of the arc of each of the sectors

Answer 1

Radius of the circle r = 120 m

Number of equal sectors = 8

∴ Central angle of each sector = `(360^circ)/"n"`

θ° =  `(360^circ)/8`

θ° = 45°

Length of the arc l =`(theta^circ)/(360^circ) xx 2pi"r units"`

= `(45^circ)/(360^circ) xx 2pi xx 120  "m"`

Length of the arc = 30 × πm

Another method:

l = `1/"n" xx 2pi"r"`

= `1/8 xx 2 xx pi xx 120`

= 30 πm

Length of the arc = 30 πm