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

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Math Expert
Joined: 02 Sep 2009
Posts: 47001
As shown in the figure above, a circular flower bed lies in a square [#permalink]

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27 Nov 2017, 23:29
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95% (01:21) correct 5% (02:46) wrong based on 20 sessions

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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

Attachment:

2017-11-28_1023_001.png [ 3.32 KiB | Viewed 569 times ]

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

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28 Nov 2017, 00:19
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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29 Nov 2017, 18:17
1
Bunuel wrote:

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

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.

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Re: As shown in the figure above, a circular flower bed lies in a square   [#permalink] 29 Nov 2017, 18:17
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