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# A circle is inscribed in a square. The area outside the

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Director
Joined: 11 Jun 2007
Posts: 932
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A circle is inscribed in a square. The area outside the [#permalink]  20 Oct 2007, 16:38
A circle is inscribed in a square. The area outside the circle is what percent of the total area of the square (approximately)?

14%
18%
22%
28%
30%

i dont understand the solution. i think a picture/diagram would help. thanks!
Senior Manager
Joined: 04 Jan 2006
Posts: 280
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Kudos [?]: 20 [0], given: 0

Re: circle [#permalink]  20 Oct 2007, 17:36
beckee529 wrote:
A circle is inscribed in a square. The area outside the circle is what percent of the total area of the square (approximately)?

14%
18%
22%
28%
30%

i dont understand the solution. i think a picture/diagram would help. thanks!

You can draw a circle inscribed in a square. Let assume that each side of the square = x
Therefore, the area of the square = x^2
Therefore, the area of the circle = Pi * r^2 = Pi * (x/2)^2
The area out side the circle = Area(square) - Area(circle) = x^2 - Pi*(x/2)^2
Percent(area outside circle/area of square) = [x^2 - Pi(x/2)^2]/x^2
= 1 - Pi/4 = 1 - 3.14/4 or approximately 0.22 = 22%
Director
Joined: 11 Jun 2007
Posts: 932
Followers: 1

Kudos [?]: 70 [0], given: 0

Re: circle [#permalink]  20 Oct 2007, 17:41
devilmirror wrote:
beckee529 wrote:
A circle is inscribed in a square. The area outside the circle is what percent of the total area of the square (approximately)?

14%
18%
22%
28%
30%

i dont understand the solution. i think a picture/diagram would help. thanks!

You can draw a circle inscribed in a square. Let assume that each side of the square = x
Therefore, the area of the square = x^2
Therefore, the area of the circle = Pi * r^2 = Pi * (x/2)^2
The area out side the circle = Area(square) - Area(circle) = x^2 - Pi*(x/2)^2
Percent(area outside circle/area of square) = [x^2 - Pi(x/2)^2]/x^2
= 1 - Pi/4 = 1 - 3.14/4 or approximately 0.22 = 22%

thanks i see where i misunderstood.. that "area outside the circle" screwed me up should just be 1 - ratio of area of circle: area of square.. duh!
Re: circle   [#permalink] 20 Oct 2007, 17:41
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