Question

The radius of a circle is 3 inches. What is the length of a 45° arc?

Answer 1

`(3\pi)/(4)\:\text{inches}`

Explanation:

The length of an arc is a part of the circle's circumference.

The circumference of a circle is equal to
`2\pi r`, where
`r` is the radius of the circle. Therefore, the circumference of the circle is
`2\pi(3)=6\pi`.

Since there are 360 degrees in a circle, the length of a 45 degree arc is equal to
`(45)/(360)` of the circumference.

Thus, the length of the arc is equal to
`(45)/(360)\cdot6\pi =\boxed{(3\pi)/(4)\:\text{inches}}`.