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

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CEO
Joined: 21 Jan 2007
Posts: 2760
Location: New York City
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Kudos [?]: 383 [0], given: 4

The area of a circle is equal to the area of a square. Which [#permalink]  13 Nov 2007, 05:24
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
Joined: 06 Mar 2006
Posts: 497
Followers: 7

Kudos [?]: 92 [0], given: 1

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
Manager
Joined: 01 Nov 2007
Posts: 69
Followers: 1

Kudos [?]: 3 [0], given: 0

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)
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