Question

A circle has a radius of 5 meters. What the length of an arc of that circle that is captured by a central angle that measures 120°?

Answer 1

10.5 metres

Explanation:

To find the circumference of a circle `=>` `pi`d

Radius =5, so diameter=10

`=>` c=10`pi`

The angle is 120, so the arc is `120/360xx10pi`

=`10/3pi`

=10.47197551

Answer 2

`"Arc Length" = (10pi)/3 ~~ 10.47 \ m`

Explanation:

If the circle has radius `5 \ m` then the total arc length of the entire circle (ie the perimeter) is given by the standard formula:

`P_"Total" = 2 pi r`

`\ \ \ \ \ \ \ \ \ = 2 xx pi xx 5`

`\ \ \ \ \ \ \ \ \ = 10 pi`

We require the length of the arc of a sector of `120^o`, we can represent this as a fraction of that of the entire circle:

`P_"Sector" = 120^0/360^0 xx P_"Total"`

`\ \ \ \ \ \ \ \ \ \ = 1/3 xx P_"Total"`

`\ \ \ \ \ \ \ \ \ \ = 1/3 xx 10 pi`

`\ \ \ \ \ \ \ \ \ \ = (10pi)/3`

`\ \ \ \ \ \ \ \ \ \ ~~ 10.47 \ m`