Question

If the central angle of a circle has measure 120° and makes a minor arc with length 6, what is the radius?

Answer 1

The radius is
`(9)/(\pi)` or 2.866

Explanation:

Given

Central angle = 120

Length of arc = 6

Required

The radius

To solve this question, we'll apply the formula of length of an arc.

The length of an arc is calculated as follows;

`L = (theta)/(360) * 2\pi r`

Where theta = central angle = 120

L = length of the arc = 6.

By substituting these values in the formula above, we have

`6 = (120)/(360) * 2\pi r`

`6 = (1)/(3) * 2\pi r`

Multiply both sides by 3

`3 * 6 =3 * (1)/(3) * 2\pi r`

`18 = 2\pi r`

Divide both sides by
`2\pi`

`(18)/(2\pi) = (2\pi r)/(2\pi)`

`r = (18)/(2\pi)`

`r = (9)/(\pi)`

Leaving the answer in terms of
`\pi`, the radius is calculated as
`(9)/(\pi)`

However, if we're to solve further

Taking
`\pi` as 3.14

`r = (9)/(3.14)`

`r = 2.866`

The radius is 2.866