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# The circumference of circle C is equal to the perimeter of square S.

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Math Expert
Joined: 02 Sep 2009
Posts: 55802
The circumference of circle C is equal to the perimeter of square S.  [#permalink]

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27 Nov 2018, 00:10
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00:00

Difficulty:

35% (medium)

Question Stats:

75% (02:14) correct 25% (02:36) wrong based on 26 sessions

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The circumference of circle C is equal to the perimeter of square S. If the area of the circle is z, which of the following represents the area of the square, in terms of z ?

A. π/(4z)

B. 4/(zπ)

C. zπ/4

D. 4π/z

E. 4z/π

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Concentration: General Management, Finance
GMAT 1: 720 Q50 V37
Re: The circumference of circle C is equal to the perimeter of square S.  [#permalink]

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27 Nov 2018, 00:26
Let the radius of circle be r and the side of square be a.
Accordingly to condition, Circumference of Circle (2πr ) = Perimeter of square (4a)
2πr = 4a
r = 4a/2π = 2a/π ----equation 1
Again, Area of circle πr^2 = z ----equation 2
π(2a/π)^2 = z (substituting 1 in 2)
a^2 = zπ/4
Area of square = a^2 = zπ/4. Hence, correct answer is option C.
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Re: The circumference of circle C is equal to the perimeter of square S.   [#permalink] 27 Nov 2018, 00:26
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