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