A gardener has 80 m of fencing wire. He can use this wire to enclose either a circular lawn or a square lawn. If he uses the entire wire in each case, what is the approximate ratio of the area of the circular lawn to the area of the square lawn?

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Accepted Answer

1. For the circle: circumference $C=80$, so radius $r=\dfrac{80}{2\pi}=\dfrac{40}{\pi}$. Area $A_c=\pi r^2=\dfrac{1600}{\pi}$.  
2. For the square: perimeter $80$, side $s=20$. Area $A_s=400$.  
3. Ratio $\dfrac{A_c}{A_s}=\dfrac{1600/\pi}{400}=\dfrac{4}{\pi}\approx1.27$.  
4. So the circular area is about $1.27:1$, choice (c).

FINAL_ANSWER: c

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