A) $ \frac{2\sqrt3}3 \cdot \fracr^2{\textArea} = 1 $ → Area ratios: $ \frac{2\sqrt3 s^2}{6\sqrt3 r^2} = \fracs^23r^2 $, and since $ s = \sqrt3r $, this becomes $ \frac3r^23r^2 = 1 $? Corrección: Pentatexto A) $ \frac{2\sqrt3}3 \cdot \fracr^2{\textArea} $ — but correct derivation: Area of hexagon = $ \frac{3\sqrt3}2 s^2 $, inscribed circle radius $ r = \frac{\sqrt3}2s \Rightarrow s = \frac2r{\sqrt3} $. Then Area $ = \frac{3\sqrt3}2 \cdot \frac4r^23 = 2\sqrt3 r^2 $. Circle area: $ \pi r^2 $. Ratio: $ \frac\pi r^2{2\sqrt3 r^2} = \frac\pi{2\sqrt3} $. But question asks for "ratio of area of circle to hexagon" or vice? Question says: area of circle over area of hexagon → $ \frac\pi r^2{2\sqrt3 r^2} = \frac\pi{2\sqrt3} $. But none match. Recheck options. Actually, $ s = \frac2r{\sqrt3} $, so $ s^2 = \frac4r^23 $. Hexagon area: $ \frac{3\sqrt3}2 \cdot \frac4r^23 = 2\sqrt3 r^2 $. So $ \frac\pi r^2{2\sqrt3 r^2} = \frac\pi{2\sqrt3} $. Approx: $ \frac3.143.464 \approx 0.907 $. None of options match. Adjust: Perhaps question should have option: $ \frac\pi{2\sqrt3} $, but since not, revise model. Instead—correct, more accurate: After calculation, the ratio is $ \frac\pi{2\sqrt3} $, but among given: - Dyverse