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In the figure above, a square is inscribed in a circle

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In the figure above, a square is inscribed in a circle [#permalink]

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New post Updated on: 02 Mar 2015, 06:32
1
3
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

79% (00:31) correct 21% (03:23) wrong based on 183 sessions

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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

********************
kudos please if you like my post...

Spoiler: :: Answer
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

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Originally posted by bumblebee14 on 01 Mar 2015, 08:31.
Last edited by bumblebee14 on 02 Mar 2015, 06:32, edited 1 time in total.
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Re: In the figure above, a square is inscribed in a circle [#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 above, a square is inscribed in a circle [#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 above, a square is inscribed in a circle [#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 above, a square is inscribed in a circle   [#permalink] 04 Mar 2018, 15:27
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