Respuesta :

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

[tex]L=2\pi r\cdot\frac{\theta}{360}[/tex]

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

[tex]\begin{gathered} 32\pi=2\pi r\cdot\frac{45}{360} \\ r=\frac{32\cdot360}{2\cdot45} \\ r=\frac{11520}{90} \\ r=128 \end{gathered}[/tex]

The radius is 128 inches long.

Now, we use the formula for circumference.

[tex]C=2\pi r[/tex]

Let's replace the radius we found before.

[tex]C=2\pi\cdot128=256\pi[/tex]

Therefore, the circumference of the circle is 256pi inches.

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