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A piece of string fits exactly once around the perimeter of a square whose area is 144. Rounded to the nearest whole number, what is the area of the largest circle that can be formed from the piece of string?

 

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 Jan 25, 2022
 #1
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We know the circumference of the circle = the perimeter of the square which is  \(\sqrt{144} =12\times4=48\) (you get 12 and 12 x 4 =48)

\(2\pi r=48\)

\(\pi r=24\)

\(r=\frac{24}{\pi}\)

\(\pi\times\frac{24}{\pi}^2=\frac{576}{\pi}\)

\(576\pi\) is about \(183\)

so 183.


 

 Jan 25, 2022

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