radius = 20 inches
angle = θ= 45°
We would apply length of an arc:
[tex]length\text{ of an arc = }\frac{\theta}{360\text{ }}\text{ }\times2\pi r[/tex][tex]\begin{gathered} \text{length of the arc = }\frac{45}{360}\times2\times\pi\times20 \\ =\text{ }\frac{1}{8}\times\text{ 40}\pi \end{gathered}[/tex]Since the options is in terms of π, the answer will be in that form
[tex]\text{length of }arc\text{ = 5}\pi\text{ inches (option B)}[/tex]