Solution: The circle’s diameter equals the square’s side, so radius $ r = \fracs2 $. Circle area: $ \pi \left(\fracs2\right)^2 = \frac\pi s^24 $. Square area: $ s^2 $. Ratio: $ \frac\frac\pi s^24s^2 = \frac\pi4 $. The ratio is $ \boxed\dfrac\pi4 $. - Crosslake