Answer
r = 14 yd
Explanation:
[tex]\begin{gathered} The\text{ }central\text{ }angle,\theta=\frac{2\pi}{7} \\ \text{The length of arc, }s=4\pi yd \\ \text{The radius of the circle, }r=? \end{gathered}[/tex]Note, the length of an arc is given by:
[tex]s=r\theta[/tex][tex]\begin{gathered} r=\frac{s}{\theta} \\ r=4\pi\div\frac{2\pi}{7} \\ r=4\pi\times\frac{7}{2\pi} \\ r=\frac{28\pi}{2\pi} \\ r=14\text{ yd} \end{gathered}[/tex]Hence, the radius of the circle is 14 yd.
