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:

$\theta_{radians}=\frac{\theta_{degrees}\pi}{180}$

Replacing the value of theta we get:

$\theta_{radians}=\frac{315\pi}{180}$

Simplifying we get:

$\theta_{radians}=\frac{7\pi}{4}$

Replacing in the formula for the arc length:

$s=(12)(\frac{7\pi}{4})$

simplifying:

$s=21\pi$