one revolution, namely one go-around the circle, is an angle of 2π radians, in radians unit of course.
now, we know the radius is 4 and 1/2 long, so, what is the "arc" made by the 2π radians angle, with that radius?
[tex]\bf \textit{arc's length}\\\\
s=r\theta \qquad
\begin{cases}
r=radius\\
\theta =angle~in\\
\qquad radians\\
------\\
\theta =2\pi \\
r=4\frac{1}{2}=\frac{9}{2}
\end{cases}\implies s=\cfrac{9}{2}\cdot 2\pi \implies s=9\pi [/tex]
