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

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In the figure below, a square is inscribed in a circle. If the area of  [#permalink]

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New post Updated on: 14 Jul 2019, 21:26
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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

Spoiler: :: Answer
Attachment:
square-in-circle.png
square-in-circle.png [ 19.04 KiB | Viewed 10081 times ]

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(2)^(1/2)]^2
= 8π

Answer is C

Originally posted by bumblebee14 on 01 Mar 2015, 08:31.
Last edited by Bunuel on 14 Jul 2019, 21:26, edited 2 times in total.
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Re: In the figure below, a square is inscribed in a circle. If the area of  [#permalink]

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New post 01 Mar 2015, 16:02
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.

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Re: In the figure below, a square is inscribed in a circle. If the area of  [#permalink]

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New post 01 Mar 2015, 23:39
Also, the question says: "In the figure above"; can you please post the figure, so that readers have clarity on this.
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Re: In the figure below, a square is inscribed in a circle. If the area of  [#permalink]

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New post 04 Mar 2018, 15:27
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:

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Re: In the figure below, a square is inscribed in a circle. If the area of  [#permalink]

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New post 15 Feb 2019, 10:13
I still dont understand the explanation : ((
Would someone be able to help pls?
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Re: In the figure below, a square is inscribed in a circle. If the area of  [#permalink]

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New post 19 Feb 2019, 16:26
1
hsn81960 wrote:
I still dont understand the explanation : ((
Would someone be able to help pls?


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
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Re: In the figure below, a square is inscribed in a circle. If the area of  [#permalink]

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New post 07 Jul 2019, 03:24
Can someone please explain why you Pythagoras theorem wouldn't work here?

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

pi[root(16)]^2 = Pi16.

Please help?
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Re: In the figure below, a square is inscribed in a circle. If the area of  [#permalink]

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New post 07 Jul 2019, 08:59
bumblebee14 wrote:
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



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
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Re: In the figure below, a square is inscribed in a circle. If the area of   [#permalink] 07 Jul 2019, 08:59
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