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# Square vs Circle

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Retired Moderator
Joined: 18 Jul 2008
Posts: 997
Followers: 8

Kudos [?]: 70 [0], given: 5

Square vs Circle [#permalink]  11 May 2009, 14:24
00:00

Difficulty:

(N/A)

Question Stats:

60% (02:07) correct 40% (02:49) wrong based on 16 sessions
The area of a square equals that of a circle. Which of the following is closest to the ratio of the diagonal of the square to the diameter of the circle?

0.95
1.26
1.40
1.57
2.51

I feel like I'm making a simple mistake somewhere, but can't figure out where.
CEO
Joined: 29 Aug 2007
Posts: 2501
Followers: 53

Kudos [?]: 505 [0], given: 19

Re: Square vs Circle [#permalink]  11 May 2009, 17:43
The area of a square equals that of a circle. Which of the following is closest to the ratio of the diagonal of the square to the diameter of the circle?

0.95
1.26
1.40
1.57
2.51

I feel like I'm making a simple mistake somewhere, but can't figure out where.

s^2 = pir^2
s = r sqrt(pi)

diagnal, ds = s (sqrt 2)
diameter, dc = 2r

ds/dc = s (sqrt 2)/2r
ds/dc = r sqrt(pi) (sqrt 2)/2r
ds/dc = sqrt(pi/2)
ds/dc = sqrt(3.14/2)
ds/dc = sqrt(1.57)
ds/dc = 1.26 approx..
_________________
Director
Joined: 23 May 2008
Posts: 840
Followers: 3

Kudos [?]: 27 [1] , given: 0

Re: Square vs Circle [#permalink]  13 May 2009, 21:32
1
KUDOS
say the area of the square and the circle =100

circle:
100=pir^2
r^2~ 33
r~5.7 (closer to 6 than 5)
diameter ~11.4

square
100=s^2
s=10
diagonal = 10sqrt2= ~1.4(10)= 14

ratio square to circle = 14/11.4 ~ 14/11 = 1.27
Manager
Joined: 22 Feb 2009
Posts: 140
Schools: Kellogg (R1 Dinged),Cornell (R2), Emory(Interview Scheduled), IESE (R1 Interviewed), ISB (Interviewed), LBS (R2), Vanderbilt (R3 Interviewed)
Followers: 8

Kudos [?]: 70 [0], given: 10

Re: Square vs Circle [#permalink]  14 May 2009, 01:08
Area of square = Area of Circle

=> (Diagnonal ^2 / 2) = Pi * Diameter^2/4
=> Diagonal/Diameter= SQRT (Pi/4)
=> Diagonal/Diameter = SQRT (1.57)
=> Diagonal/Diameter= ~1.26
Director
Joined: 27 Jun 2008
Posts: 549
WE 1: Investment Banking - 6yrs
Followers: 1

Kudos [?]: 45 [0], given: 92

Re: Square vs Circle [#permalink]  14 May 2009, 02:51
GMAT TIGER wrote:
The area of a square equals that of a circle. Which of the following is closest to the ratio of the diagonal of the square to the diameter of the circle?

0.95
1.26
1.40
1.57
2.51

I feel like I'm making a simple mistake somewhere, but can't figure out where.

s^2 = pir^2
s = r sqrt(pi)

diagnal, ds = s (sqrt 2)
diameter, dc = 2r

ds/dc = s (sqrt 2)/2r
ds/dc = r sqrt(pi) (sqrt 2)/2r
ds/dc = sqrt(pi/2)
ds/dc = sqrt(3.14/2)
ds/dc = sqrt(1.57)
ds/dc = 1.26 approx..

Agree...good explanation.
Retired Moderator
Joined: 18 Jul 2008
Posts: 997
Followers: 8

Kudos [?]: 70 [0], given: 5

Re: Square vs Circle [#permalink]  14 May 2009, 06:52
Good explanations. OA is B.
Manager
Affiliations: The Earth organization, India
Joined: 25 Dec 2010
Posts: 194
WE 1: SAP consultant-IT 2 years
WE 2: Entrepreneur-family business 2 years
Followers: 4

Kudos [?]: 10 [0], given: 12

Re: Square vs Circle [#permalink]  08 Jul 2011, 09:10
what am I doing wrong ?

area of sq = d^2/2
area of circle = pi r^2

equating we get d/r = under root(pi/2) , which is the answer

but we need d/2r so i am getting an additional 1/2 ???
_________________

Cheers !!

Quant 47-Striving for 50
Verbal 34-Striving for 40

Re: Square vs Circle   [#permalink] 08 Jul 2011, 09:10
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# Square vs Circle

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