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The area of a circle is equal to the area of a square. Which

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CEO
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The area of a circle is equal to the area of a square. Which [#permalink] New post 13 Nov 2007, 05:24
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The area of a circle is equal to the area of a square. Which of the following is closest to the ratio of the diag of the sq to the diameter of the circle?

.95
1.26
1.4
1.57
2.51
Senior Manager
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 [#permalink] New post 13 Nov 2007, 06:08
pi r^2=s^2
pick a number let's assume s=2
s^2=4 diagonal =2 sqrt2
pi r^2=4 r=sqrt(4/pi) diameter=2*sqrt(4/pi)
diag/diameter is approximately 1.2
So, answer B would be the closest answer.
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 [#permalink] New post 13 Nov 2007, 06:56
Consider D = dia of circle
S = Diagonal of square
s = side of square
s^2 + s^2 = S^2
2s^2 = S^2
s^2 (area of square) = (S^2)/2

Area of circle = (Pi/4)D^2

equating Areas we get S^2/D^2 = Sqrt(Pi/2)

= 1.252
Appox 1.26 (B)
  [#permalink] 13 Nov 2007, 06:56
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The area of a circle is equal to the area of a square. Which

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