Question

If the circumference of a circle is 12, and the angle measure of an arc is 60°, what is the length of the arc?

Answer 1

the length of the arc is 2

Explanation:

As a circle is `360^o` and `60^o` is `1/6` of that, the length of the arc will also be `1/6` of the full circle, i.e. `12/6=2`

Answer 2

Length of arc= `theta xx pi/180 xx r`
Circumference=`2pir`

`12=2pir`
`12/2=pir`

`6=pir`

`6=(22r)/7`

`6xx7=22r`

`42=22r`

`42/22=r`

`r=21/11cm`

Length of arc`= 60 xx (22/7)/180 xx 21/11`

Length of arc`=60 xx 22/(7xx180)xx21/11`

Length of arc`=cancel (60) xx cancel (22)/cancel(1260) xx 21/cancel(11)`

Length of arc`= 1 xx 2/cancel(21) xx cancel(21)/1`

Length of arc= 2cm