SOLUTION: The perimeter of a particular square and the circumference of a particular circle are equal. What is the ratio of the area of the square to the area of the circle? Express your ans
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Question 217496: The perimeter of a particular square and the circumference of a particular circle are equal. What is the ratio of the area of the square to the area of the circle? Express your answer as a common fraction in terms of π.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
perimeter of square equals
perimeter of circle =
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we have since the perimeters of both the square and the circle are equal.
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this makes
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area of square equals
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area of circle equals
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ratio of area of square to area of circle equals
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we simplify this to get:
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area of square / area of circle =
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this means area of square = area of circle *
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this also means area of circle = area of square *
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to test, we need a circle with a perimeter the same as a square.
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let a side of our square = 7
perimeter of the square is
perimeter of our circle must be 28
this means the radius of our circle equals
this means the area of our circle equals
the area of our square is
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the ratio holds.
the answer is that the ratio of the area of the square to the area of the circle is
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