We are asked to find the length of the arc on a circle
Radius = r = 12 inches
Central Angle = θ = 45°
The arc length on a circle is given by
[tex]arc=2\cdot\pi\cdot r(\frac{\theta}{360\degree})[/tex]Let us substitute the given values of r and θ
[tex]\begin{gathered} arc=2\cdot\pi\cdot r(\frac{\theta}{360\degree}) \\ arc=2\cdot\pi\cdot12(\frac{45\degree}{360\degree}) \\ arc=24\cdot\pi(\frac{1\degree}{8\degree}) \\ arc=\frac{24\cdot\pi}{8} \\ arc=3\pi \end{gathered}[/tex]Therefore, the arc length is found to be 3π inches.
