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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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

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

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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 circular region?

(A) 2π
(B) 4π
(C) 8π
(D) 12π
(E) 16π

OA C

Source: GMAT Prep

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Source: Beat The GMAT — Problem Solving | Mon Jun 14, 2021 4:19 pm

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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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