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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] New post 08 Nov 2012, 22:56
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Question Stats:

74% (02:42) correct 26% (02:31) wrong based on 80 sessions
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] New post 09 Nov 2012, 00:06
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] New post 09 Jul 2014, 19:52
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A circle and a square have the same area. What is the ratio [#permalink] New post 09 Jul 2014, 23:54
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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

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A circle and a square have the same area. What is the ratio   [#permalink] 09 Jul 2014, 23:54
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