Since the central angle is a right angle, the labeled arc is 1/4 of the total circumference of the circle. The circumference of a circle with radius [tex]r[/tex] is [tex]2\pi r[/tex], so we have
[tex]\dfrac{2\pi r}4=18\pi\,\mathrm{in}\implies r=36\,\mathrm{in}[/tex]
