Use the arc length formula:

\(L=2πr\cdot(\theta/360°)\)

where r is the radius and \(\theta\) is the central angle.

Subtitute \(L=6.5\) cm and \(\theta=45^\circ\) then solve for r:

\(6.5=(π/4)r\)

Multiply both sides by \(4/π\):

\(6.5\cdot(4/π)=r\)

\(r \sim 8.3\ cm\)