If the circumference of a circle is 24 and the angle measure of an arc is 120 which is the length of the arc?

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Answer 1 · 2018-03-18T01:53:13

Let the radius of the circle be #r#

So its circumference will be
#2pir=24#

#=>r=24/(2pi)#

Now the length of the arc which subtends an angle of #120^@=(120*pi)/180# radian at the center will be
#=(120*pi)/180xx"radius"#

#=(120*pi)/180xx24/(2pi)#

#=8#

Answer 2 · 2018-03-18T12:34:03

See another process below for answering this problem.

There are #360^o# in a complete circle and the circumference is #24#..

The arc angle we are told is #120^o# and therefore the arc length is:

#120^o/360^o * 24 =>#

#2880^o/360^o =>#

#2880^color(red)(cancel(color(black)(o)))/360^color(red)(cancel(color(black)(o))) =>#

#2880/360 =>#

#8#