1 Answer

Ramiro Magno · Answer 1 · 2023-11-17T00:38:28+0000

First, we have to find the radius of the circle. Let's use the arc length formula.

$L=2\pi r\cdot(\theta)/(360)$

Where L = 32 pi inches, theta = 45. Let's use this information and solve for r.

$\begin{gathered} 32\pi=2\pi r\cdot(45)/(360) \\ r=(32\cdot360)/(2\cdot45) \\ r=(11520)/(90) \\ r=128 \end{gathered}$

The radius is 128 inches long.

Now, we use the formula for circumference.

$C=2\pi r$

Let's replace the radius we found before.

$C=2\pi\cdot128=256\pi$