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Britt has a square plot measuring 660 feet on a side, which he wants to irrigate. Long ago, he used fences to divide the plot into four equal-sized square fields. He has two choices. He can tear down the fences and use one long pivot-arm sprinkler that will irrigate a large circle centered at the middle of the plot. Otherwise, he can leave the fences up and irrigate each field separately with smaller pivot sprinklers. What is the difference in irrigated area between the two options?

Explanation

If he takes down the fences, the farmer can irrigate a circle 330 feet in radius for an area of 342,119 square feet. If he leaves his fences, he gets four circles with radii of 165 feet. Each small circle has an area of 85,530 square feet, or 342,119 total square feet. There is no difference.

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