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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]  18 Jul 2018, 09:38
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#greprepclub In the figure above, the circle is inscribed in a square.jpg [ 16.42 KiB | Viewed 2669 times ]

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]  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]  21 Jul 2018, 03:26
b is greater
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Re: In the figure above, the circle is inscribed in a square tha [#permalink]  18 Jan 2019, 21:20
B
Re: In the figure above, the circle is inscribed in a square tha   [#permalink] 18 Jan 2019, 21:20
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