A farmer is putting up a fence for her animals. She orginally had the fence enclosing a square was 18ft by 18ft. Suppose she uses the same amount of fencing to enclose a circular area. What is the area of the circle?

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First look: More than 324 square feet :) Now, [latex]l=2\pi*r[/latex] which means that [latex]r=\frac{l}{2\pi}[/latex]. But l is the original perimeter, 4 times the side of the square, that is, 72 ft. So, [latex]r=\frac{72}{2\pi}=\frac{36}{\pi}[/latex] Now, the area of that circle is [latex]A=\pi*r^2=\pi*\frac{1296}{\pi^2}=\frac{1296}{\pi}[/latex], which is about 412.5 square feet. It's true, that's more (that's the most you can actually get with that amount of fence :) )

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