Question

Leave answer in terms of pi or as a fraction.

Answer 1

We are asked to find the arc length of a segment of a circle, to do that let's remember the formula for the arclength of a circle:

`s=r\theta`

Where the greek letter theta represents the angle in radians. Since we are given the angle in degrees we need to transform it using the following relationship:

`\theta_(radians)=(\theta_(degrees)\pi)/(180)`

Replacing the value of theta we get:

`\theta_(radians)=(315\pi)/(180)`

Simplifying we get:

`\theta_(radians)=(7\pi)/(4)`

Replacing in the formula for the arc length:

`s=(12)((7\pi)/(4))`

simplifying:

`s=21\pi`