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A gardener has 80 m of fencing wire and can enclose with it either a circular plot or a square plot, using all the wire in each case. Approximately what is the ratio of the area of the circular plot to the area of the square plot?

1. 1 : 1
2. 1.21 : 1
3. 1.27 : 1
4. 1.57 : 1

Correct answer: 1.27 : 1

Solution

With equal perimeters, circle area / square area = (P^2/4pi)/(P^2/16) = 16/(4pi) = 4/pi which is about 1.273. So the ratio is roughly 1.27 : 1.

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