Question

A circle has a radius of 12.6 cm What is the exact length of an arc formed by a central angle measuring 120°? Express your answer using π

Answer 1

`8.4pi`

Explanation:

I went ahead and drew a diagram of this problem:

The formula to find the length of an arc is:

`m^@/360^@ 2pir`

`m = "degree measure of arc"`
`r = "radius"`

They gave that degree measure of the central angle as `120^@`. An arc bounded by a central angle has the same measure as the angle, so the measure of the arc is also `120^@`.

And the radius is `12.6`, so we can put both of these values into the formula:

`m/360 2pir`

`120/360 2pi(12.6)`

`120/360 25.2pi`

Simplify `120/360` to `1/3`, and finish the other simplifying:

`1/3 25.2pi`

`25.2/3pi`

`8.4pi`

Since they want the answer expressed by `pi`, `8.4pi` is the answer.