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In the figure below, a square is inscribed in a circle. If the area of the square region is 16, what is the area of the

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by BTGmoderatorDC » Mon Jun 14, 2021 4:19 pm

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square-in-circle.png
In the figure below, a square is inscribed in a circle. If the area of the square region is 16, what is the area of the circular region?


(A) 2π
(B) 4π
(C) 8π
(D) 12π
(E) 16π


OA C

Source: GMAT Prep
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Re: In the figure below, a square is inscribed in a circle. If the area of the square region is 16, what is the area of

by swerve » Tue Jun 15, 2021 8:27 am
BTGmoderatorDC wrote: ↑
Mon Jun 14, 2021 4:19 pm
 square-in-circle.png

In the figure below, a square is inscribed in a circle. If the area of the square region is 16, what is the area of the circular region?


(A) 2π
(B) 4π
(C) 8π
(D) 12π
(E) 16π


OA C

Source: GMAT Prep
The radius of the circle is \(\dfrac{1}{2}\) diameter

Here the diagonal of the square \(= a\sqrt{2}=4\sqrt{2},\) is the diameter of the circle.

The radius of the circle is \(\dfrac{1}{2}\cdot 4\sqrt{2}=2\sqrt{2}\)

Area of the circle \(= \pi \cdot r^2=π\cdot (2\sqrt{2})^2 = 8\pi\)

Therefore, C
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