Solution
Given length or arc = 6π
The formula for length of arc is
[tex]\begin{gathered} L_{Arc}=\frac{\theta}{360}\times2\pi r \\ \\ \text{ since }L_{Arc}=6\pi \\ \\ \theta=180 \end{gathered}[/tex][tex]\begin{gathered} \Rightarrow6\pi=\frac{180}{360}\times2\pi r \\ \\ \Rightarrow r=\frac{6\pi\times360}{180\times2\pi}=6 \end{gathered}[/tex]
Hence, the length of the radius is 6 units
