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

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Bunuel
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If the area of square S and the area of circle C are equal, then the r [#permalink] New post   26 Apr 2020, 02:46
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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. 1/2
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C
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Re: If the area of square S and the area of circle C are equal, then the r [#permalink] New post   26 Apr 2020, 03:03
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Answer is supposedly C
Area of square S = S^2
Area of Circle = πr^2
S^2=πr^2
S=√π*r ------(1)
Now perimeter of Square and circle.
4S/2πr
Putting Value from equation 1
4√π*r/2πr
2/√π
2*√7/√22
1.1281. (approximate value)

Only option C have the nearest value among all 5. Which is 1.125

So answer should be C

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Re: If the area of square S and the area of circle C are equal, then the r [#permalink] New post   26 Apr 2020, 03:40
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Bunuel 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. 1/2


s^2 = πr^2

i.e. (s/r)^2 = π

i.e. (s/r) = √π

Ratio of perimeter to circumference = 4s / 2πr = (4/2π)*(s/r) = (2/π)*(√π) = 2/√π ≈2/1.7 = 20/17 ≈ 9/8

Answer:Option C
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Re: If the area of square S and the area of circle C are equal, then the r [#permalink] New post   26 Apr 2020, 14:11
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Bunuel 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. 1/2


Let the area of S be 1. Then the perimeter of S is 4, the radius of C is \(\sqrt{\frac{1}{ \pi}}\) and the circumference of C is \(2\pi * \frac{1}{\sqrt{ \pi}} = 2\sqrt{\pi} \).

Then the ratio is \(\frac{4}{2\sqrt{\pi}} = \frac{2}{\sqrt{\pi}}\).

The hard part is estimating \(\sqrt{\pi}\), since we know \(\sqrt{324} = 18\), we have \(\sqrt{3.24} = 1.8\), so 1.8 is a close approximate of \(\sqrt{\pi}\). Then we are approximating 2/1.8 = 10/9, C is a very close answer.

Ans: C
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If the area of square S and the area of circle C are equal, then the r [#permalink] New post   26 Apr 2020, 23:51
S^2=pi*r^2-- eq 1

to find
4s/2pi*r
squaring both D and N
16s^2/4*pi^2*r^2
substituting the value of s^2 from eq 1
16*pi*r^2/4*pi^2*r^2
4/pi
remember we had squared above
2/root pi

ans C
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Re: If the area of square S and the area of circle C are equal, then the r [#permalink] New post   16 Jul 2021, 02:03
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Let us take a circle with radius = 2 units

Let us have a square with side = √4π units

Their areas are equal, each being equal to 4π square units

The ratio of the perimeter of square and circle is 4 * √4π / 4π

= 2 / √π (Eliminate A,B,E as the values would be way too less than the required and that too between 0 and 1)

= 2/1.8 (approximately) Eliminate D

(option c)

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Re: If the area of square S and the area of circle C are equal, then the r [#permalink]
16 Jul 2021, 02:03
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