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If a square of side x and a circle of radius r have equal areas, what

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If a square of side x and a circle of radius r have equal areas, what  [#permalink]

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New post 10 Jan 2019, 02:57
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

89% (00:50) correct 11% (01:05) wrong based on 24 sessions

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Location: India
Re: If a square of side x and a circle of radius r have equal areas, what  [#permalink]

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New post 10 Jan 2019, 03:51
If a square of side x and a circle of radius r have equal areas, what is the ratio x/r ?

Area of the square of side \(x = x^2\)
Area of the Circle of radius \(r = Pi*r^2\)
Both are equal implies
\(x^2 = Pi*r^2\)
\(x/r = \sqrt{Pi}\)

Option B is correct
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Re: If a square of side x and a circle of radius r have equal areas, what  [#permalink]

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New post 10 Jan 2019, 06:43

Solution


Given:
    • Side of a square = x
    • Radius of a circle = r
    • Both square and circle have equal areas

To find:
    • The ratio of \(\frac{x}{r}\)

Approach and Working:
    • Area of square = \(x^2\)
    • Area of circle = \(ᴨr^2\)
    • We are given that, \(ᴨr^2 = x^2\)

Thus, \(\frac{x}{r} = √ᴨ\)

Hence, the correct answer is Option B

Answer: B

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Re: If a square of side x and a circle of radius r have equal areas, what  [#permalink]

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New post 10 Jan 2019, 07:16
Bunuel wrote:
If a square of side x and a circle of radius r have equal areas, what is the ratio x/r ?


A. \(\frac{2}{\pi}\)

B. \(\sqrt{\pi}\)

C. \(\frac{\pi}{2}\)

D. \(\pi\)

E. \(\pi^2\)


x^2= pi * r^2
x/r = sqrt pi
IMO B
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Re: If a square of side x and a circle of radius r have equal areas, what   [#permalink] 10 Jan 2019, 07:16
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