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As shown in the figure above, a circular flower bed lies in a square

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As shown in the figure above, a circular flower bed lies in a square [#permalink]

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New post 27 Nov 2017, 22:29
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As shown in the figure above, a circular flower bed lies in a square garden that is 60 meters on each side. What fraction of the garden plot area is not part of the flower bed?

(A) 1/4
(B) 3/4
(C) (4 – π)/2
(D) (4 – π)/4
(E) (π – 2)/4


[Reveal] Spoiler:
Attachment:
2017-11-28_1023_001.png
2017-11-28_1023_001.png [ 3.32 KiB | Viewed 242 times ]
[Reveal] Spoiler: OA

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Re: As shown in the figure above, a circular flower bed lies in a square [#permalink]

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New post 27 Nov 2017, 23:19
D

Area of square = 3600 m^2

Area of circle with diameter as 60=pi.60^2/4
=900.pi

Fraction that is not flower bed is 3600-900.pi/3600
=900(4-pi)/3600
=(4-pi)/4



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Re: As shown in the figure above, a circular flower bed lies in a square [#permalink]

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New post 29 Nov 2017, 17:17
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Bunuel wrote:
Image
As shown in the figure above, a circular flower bed lies in a square garden that is 60 meters on each side. What fraction of the garden plot area is not part of the flower bed?

(A) 1/4
(B) 3/4
(C) (4 – π)/2
(D) (4 – π)/4
(E) (π – 2)/4

[Reveal] Spoiler:
Attachment:
2017-11-28_1023_001.png


Since side = 60, the diameter of the circle is also 60 and so the radius is 30.

The area of the square is 60 x 60 = 3600 and the area of the circle is π x 30^2 = 900π.

The part of the plot that is not part of the bed is (area of square) - (area of circle) = 3600 - 900π = 900(4 - π)

So the fraction of the garden plot area that is not part of the flower bed is 900(4 - π)/3600 = (4 - π)/4.

Answer: D
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Kudos [?]: 1024 [1], given: 3

Re: As shown in the figure above, a circular flower bed lies in a square   [#permalink] 29 Nov 2017, 17:17
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As shown in the figure above, a circular flower bed lies in a square

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