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

Question

https://gmatclub.com/forum/download/file.php?id=25690 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 square-in-circle.png Answer: Area of a square = (Diagonal)^2 /2 16 = (Diagonal)^2 /2 32 = (Diagonal)^2 Diagonal = 4 (2)^(1/2) Diagonal = Diameter in the given figure Radius = Diameter/2 Radius = 2(2)^(1/2) Area of a circle = πr^2 = π ^2 = 8π Answer is C

sashiim20 · Accepted Answer

Let side of Square be  = a

Radius of Circle  = r

Area of square  = a^2= 16

Side of square  = a = 4

Diagonal of square  = 4\sqrt{2}

Diagonal of square  =  Diameter of circle

4\sqrt{2} = 2r

r = \frac{4\sqrt{2}}{2} = 2\sqrt{2}

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

Answer C

EMPOWERgmatRichC · Answer

Hi bumblebee14,

It's great that you posted this question. However, by posting your explanation (and the correct answer) immediately under it, it's difficult for any of the other users to avoid looking at your answer. I'd suggest that you post all of that as a 'spoiler', so that others can attempt this question without any part of the explanation staring them right in the face.

GMAT assassins aren't born, they're made,
Rich

sukanyar · Answer

Also, the question says: "In the figure above"; can you please post the figure, so that readers have clarity on this.

EMPOWERgmatRichC · Answer

Hi All,

In these types of multi-shape questions, it's usually a must to focus on the radius of the circle. Do you know it's value? Can you figure it out? How does the radius "interact" with the other shape(s)?

Here, we know that the area of the square is 16, so each side of the square = 4.

The diagonal of the square = the diameter of the circle. So….

4(root2) = diameter 
2(root2) = radius

Next, plug the radius into the formula for area of a circle: pi(radius)^2

pi(2root2)^2 = 8pi

Final Answer:  C

GMAT assassins aren't born, they're made, 
Rich

hsn81960 · Answer

I still dont understand the explanation : ((
Would someone be able to help pls?

nanial · Answer

Isosceles is 1:1:root2

so diagonal(and diameter) is 4(root2)

R = 1/2 diameter means diameter is 2root2
Plug into pi r^2

First find r^2 = 2^2(root2)^2 = 2*4
2*4Pi = 8pi

hanutsingh · Answer

Can someone please explain why you Pythagoras theorem wouldn't work here?

4^2 + 4^2 = 32
root(32) = diameter
Root(16)=radius

pi ^2 = Pi16.

Please help?

jmwon · Answer

I made the same error as you did. Pythagoras does work here, but 16π is a wrong from calculation error.

4^2 + 4^2 = c^2 
 16 + 16 = c^2  (--> THIS DOES NOT EQUATE TO C = 16!)
 32 = c^2 
 c = 4 \sqrt{2}

c = the diameter (d) of this circle. Need the radius which is  \frac{d}{2} .
 r = \frac{4 \sqrt{2}}{2} 
 r = 2 \sqrt{2}

Now plug in our radius amount into the circle area formula  A = π r^2 
 A = π (2 \sqrt{2})^2 
  = π (4 * 2) 
 = 8π

dcummins · Answer

radius of circle = 4 root 2 / 2

CrackverbalGMAT · Answer

Radius of the circle is  \frac{1}{2} * diameter

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

Radius of the circle is  \frac{1}{2} * 4\sqrt{2} = 2\sqrt{2}

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

Option C

Arun Kumar

sumaiyabss · Answer

Given,
 Area of square =16
 So, 
 S^2 = 16
 S = √16
 =4

As we know,
  Diameter of Circle = Diagonal of Square

So, 
2r = 4S
2r = 4*4    
2r = 8
r = 8÷2
 = 4

So, area of square = πr^2
 = π×4^2
 = π×8
 = π8

Ans:8π

bumpbot · Answer

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

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