The arc length, when the central angle is measure in degrees, is given by:
[tex]s=2\pi r(\frac{\theta}{360})[/tex]
In this case the arc length is 19.6 cm and the angle is 130°, plugging these values we have that:
[tex]\begin{gathered} 19.6=2\pi r(\frac{130}{360}) \\ r=(\frac{19.6}{2\pi})(\frac{360}{130}) \\ r=8.6 \end{gathered}[/tex]
Therefore, the radius is 8.6 cm
