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# A circle and a square have the same area. What is the ratio

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A circle and a square have the same area. What is the ratio [#permalink]

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08 Nov 2012, 23:56
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45% (medium)

Question Stats:

73% (02:41) correct 27% (02:27) wrong based on 83 sessions

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What is the ratio of the diameter of the circle to the diagonal of the square - the area of the square and circle is equal?

(A) 2 : √(2pi)
(B) 1 : 2√pi
(C) 2√pi : √2
(D) 1 : √2
(E) 1 : 2(pi)
[Reveal] Spoiler: OA

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Re: A circle and a square have the same area. What is the ratio [#permalink]

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09 Nov 2012, 01:06
Pansi wrote:
What is the ratio of the diameter of the circle to the diagonal of the square - the area of the square and circle is equal?

(A) 2 : √(2pi)
(B) 1 : 2√pi
(C) 2√pi : √2
(D) 1 : √2
(E) 1 : 2(pi)

Diameter be D and diagonal be y then D/Y = ?
given is area of square = area of circle
=> 1/2*Y^2 = 1/4*pi*D^2
=>D/Y= sqrt(2/pi) = 2/sqrt(2pi)

Ans A it is.
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Re: A circle and a square have the same area. What is the ratio [#permalink]

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09 Jul 2014, 20:52
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A circle and a square have the same area. What is the ratio [#permalink]

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10 Jul 2014, 00:54
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Refer diagram below:

$$\pi r^2 = a^2$$

$$a = \sqrt{\pi}r$$

$$\frac{Diameter of circle}{Diagonal of Square} = \frac{2r}{\sqrt{2} \sqrt{\pi}r}$$

$$Answer = \frac{2}{\sqrt{2 \pi}$$ = A
Attachments

pi.png [ 4.75 KiB | Viewed 950 times ]

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A circle and a square have the same area. What is the ratio   [#permalink] 10 Jul 2014, 00:54
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