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# If the area of square S and the area of circle C are equal,

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If the area of square S and the area of circle C are equal, [#permalink]

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30 Nov 2007, 14:17
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67% (00:02) correct 33% (00:00) wrong based on 6 sessions

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If the area of square S and the area of circle C are equal, then the ratio of the perimeter of S to the circumference of C is closest to

a) 7/9
b) 8/9
c) 9/8
d) 4/3
e) 2/1

Can someone show me the algebraic way? or perhaps any other way that you are at least familiar with? thanks

Last edited by tarek99 on 30 Nov 2007, 15:29, edited 1 time in total.

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SVP
Joined: 05 Jul 2006
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Re: PS: Circle and Square [#permalink]

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30 Nov 2007, 14:59
tarek99 wrote:
If the area of square S and the area of circle C are equal, then the ratio of the perimeter of S to the circumference of C is closest to

a) 7/9
b) 8/9
c) 9/8
d) 4/3
e) 2/1

Can someone show me the algebraic way? or perhaps any other way to you are at least familiar with? thanks

s^2 = pir^2 what is ( 4s/2pir) = 2s/ pi r?

s^2/r^2 = pi

2sr^2/ rs^2 = 2r/s

then ??????????/ too late here and flying tomorrow . have a look at my approach

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SVP
Joined: 21 Jul 2006
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01 Dec 2007, 03:39
well, the OA is C, but I don't know how. This is what i've done so far:

S^2=Pi*r^2 then sqrt both sides to get S in terms of the circle:

s= sqrt(pi)r so this is our side of square. then multiply by 4 to get the perimeter of the square:

Perimeter of square: 4r*sqrt(pi)

therefore, the ratio of the perimeter of square to cirum. of circle should be:

4r*sqrt(pi) / 2r*pi = 2*sqrt(pi)/pi or 2/sqrt(pi), but because we can't leave the sqrt sign in the denominator, we leave it as 2*sqrt(pi)/pi which is no where close to the OA. so can anyone help me out here??? i'd really appreciate it.

Kudos [?]: 978 [0], given: 1

Director
Joined: 26 Jul 2007
Posts: 535

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Schools: Stern, McCombs, Marshall, Wharton

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07 Dec 2007, 13:36
tarek99 wrote:
well, the OA is C, but I don't know how. This is what i've done so far:

S^2=Pi*r^2 then sqrt both sides to get S in terms of the circle:

s= sqrt(pi)r so this is our side of square. then multiply by 4 to get the perimeter of the square:

Perimeter of square: 4r*sqrt(pi)

therefore, the ratio of the perimeter of square to cirum. of circle should be:

4r*sqrt(pi) / 2r*pi = 2*sqrt(pi)/pi or 2/sqrt(pi), but because we can't leave the sqrt sign in the denominator, we leave it as 2*sqrt(pi)/pi which is no where close to the OA. so can anyone help me out here??? i'd really appreciate it.

I picked numbers and approximated for this one.

Let the side of the square = 3
Then 3*3=pi*r^2

If you solve for r you get 3/(sqrt(pi))

So the ration of perimeter to circum. should be 4s/2*pi*r.

Fill in you values and you get 12/2*pi*(sqrt(pi)).

If you reduce you get 2sqrt(pi)/pi. Just aproximate 3.14 for pi and 1.75 for sqrt(pi) and you get 3.5/3.14 or a little more than one. Ans C

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SVP
Joined: 28 Dec 2005
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13 Dec 2007, 20:31
tarek99 wrote:
well, the OA is C, but I don't know how. This is what i've done so far:

S^2=Pi*r^2 then sqrt both sides to get S in terms of the circle:

s= sqrt(pi)r so this is our side of square. then multiply by 4 to get the perimeter of the square:

Perimeter of square: 4r*sqrt(pi)

therefore, the ratio of the perimeter of square to cirum. of circle should be:

4r*sqrt(pi) / 2r*pi = 2*sqrt(pi)/pi or 2/sqrt(pi), but because we can't leave the sqrt sign in the denominator, we leave it as 2*sqrt(pi)/pi which is no where close to the OA. so can anyone help me out here??? i'd really appreciate it.

i took exactly this approach. anyone else care to give this a shot ?

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Manager
Joined: 03 Sep 2006
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13 Dec 2007, 20:47
I went the same way as tarek99 and left with 2 / sqrt (Pi)

So yesterday I learned that I need to know sqrt of Pi for some questions here, and sqrt of Pi ~ 1.77

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CEO
Joined: 29 Mar 2007
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Re: PS: Circle and Square [#permalink]

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13 Dec 2007, 23:19
tarek99 wrote:
If the area of square S and the area of circle C are equal, then the ratio of the perimeter of S to the circumference of C is closest to

a) 7/9
b) 8/9
c) 9/8
d) 4/3
e) 2/1

Can someone show me the algebraic way? or perhaps any other way that you are at least familiar with? thanks

Square: A=s^2
Circle: A=pir^2

s^2=pir^2

4s=perimeter and 2pir=circumfrence

4s/2pir =? solve for either variable.

r= s/sqrtpi -> 4s/2pi(s/sqrtpi) --> (4s*sqrtpi)/2pis -> 2/sqrtpi --> 2sqrtpi/pi -> 2*1.7/3 --> 3.6/3 ~1.2

u can elimante a few choices ABE. DC, well if u know 4/3=1.333 then it could be it.

9/8 = 1.125

So C is closest.

To be honest, b/c 4/3 looked very similar to 3.6/3, I chose it =(.

Gotta check those!!!

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Re: PS: Circle and Square   [#permalink] 13 Dec 2007, 23:19
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