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If the area of a square equals the area of a circle, which of the foll [#permalink]
11 May 2009, 14:24

4

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

85% (hard)

Question Stats:

44% (02:36) correct
56% (02:45) wrong based on 66 sessions

If the area of a square equals the area of a circle, which of the following is closest to the ratio of the diagonal of the square to the diameter of the circle?

Re: If the area of a square equals the area of a circle, which of the foll [#permalink]
11 May 2009, 17:43

bigfernhead 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.

Re: If the area of a square equals the area of a circle, which of the foll [#permalink]
14 May 2009, 02:51

GMAT TIGER wrote:

bigfernhead 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.

Re: If the area of a square equals the area of a circle, which of the foll [#permalink]
01 Oct 2014, 23:29

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Re: If the area of a square equals the area of a circle, which of the foll [#permalink]
02 Oct 2014, 02:46

Expert's post

bigfernhead wrote:

If the area of a square equals the area of a circle, which of the following is closest to the ratio of the diagonal of the square to the diameter of the circle?

A. 0.95 B. 1.26 C. 1.40 D. 1.57 E. 2.51

M19-21

If \(x\) is the side of the square, then the area of the square is \(x^2\) and the diagonal of the square is \(x\sqrt{2}\). If \(d\) is the diameter of the circle then the area of the circle is \(\pi(\frac{d}{2})^2\). Because \(x^2 = \pi(\frac{d}{2})^2\), \(d = \frac{2x}{\sqrt{\pi}}\). The required ratio \(=\frac{x\sqrt{2}}{\frac{2x}{\sqrt{\pi}}} = \frac{\sqrt{\pi}}{\sqrt{2}} = \sqrt{\frac{\pi}{2}}\) or approximately \(\sqrt{1.57}\). This is slightly smaller than \(\sqrt{1.69} = 1.3\). The best answer is therefore B.

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