Question

Find the arc length of a central angle of
`\pi`/4 in a circle whose radius is 8 inches

Answer 1

The arc length is
`2\pi` inches or 6.28 inches

Explanation:

To solve this we are using the arc length formula:

`s=r\alpha`

where

`s` is the arc length

`r` is the radius of the circle

`\alpha` is the central angle in radians

We know from our problem that the central angle is
`(\pi )/(4)` and the radius of the circle is 8 inches, so
`\alpha =(\pi )/(4)` and
`r=8in`. Let's replace the values to find
`s`:

`s=r\alpha`

`s=(8in)((\pi )/(4) )`

`s=2\pi in`

`s=6.28in`