[tex]\bf r=\cfrac{s}{\theta}\qquad
\begin{cases}
r=radius\\
s=\textit{arc's length}\\
\theta=\textit{central angle in radians}\\
----------\\
s=180\\
\theta=\textit{45 revolutions}\\
\qquad 2\pi \cdot 45\\
\qquad 90\pi
\end{cases}\implies
\begin{array}{llll}
r=\cfrac{180}{90\pi }\\\\
r=\cfrac{2}{\pi }\\\\
diameter=2r\\\\
diameter=\cfrac{4}{\pi }
\end{array} [/tex]
