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In the figure above, the circle is inscribed in a square tha

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In the figure above, the circle is inscribed in a square tha [#permalink] New post 18 Jul 2018, 09:38
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In the figure above, the circle is inscribed in a square that has area 16.

Quantity A
Quantity B
The area of the shaded region
1


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

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[Reveal] Spoiler: OA

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Re: In the figure above, the circle is inscribed in a square tha [#permalink] New post 19 Jul 2018, 01:46
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We are given that the area of the square is \(16\) hence it must be that each side of the square is \(4\)
Since the circle is inscribed in the square the diameter of the circle equals the length of a side of the square.

Therefore, the radius of the circle \(= 2\)

area of the circle is \(\pi r^2 = \pi 2^2 = 4\pi\)
subtracting area of the circle from the area of the square we get,

the combined area of the four portions outside the circle but inside the square
that area is \(16 - 4\pi\)
we are required to find the area of one of those 4 portions.
which is equal to \((16-4)\pi/4 = 4 - \pi\)
roughly \(\pi\) is \(3.14\). \(4-3.14\) = a value less than 1
Therefore option B is bigger
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Re: In the figure above, the circle is inscribed in a square tha [#permalink] New post 21 Jul 2018, 03:26
b is greater
Re: In the figure above, the circle is inscribed in a square tha   [#permalink] 21 Jul 2018, 03:26
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In the figure above, the circle is inscribed in a square tha

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