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If the area of the square inscribed in the circle shown above is 36

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If the area of the square inscribed in the circle shown above is 36  [#permalink]

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New post 06 Sep 2018, 00:03
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If the area of the square inscribed in the circle shown above is 36, what is the area of the circle?


A. \(9\pi\)

B. \(18\pi\)

C. \(\sqrt{72} \pi\)

D. \(4\sqrt{18} \pi\)

E. \(36\pi\)

Spoiler: ::
Attachment:
image009.jpg
image009.jpg [ 1.76 KiB | Viewed 444 times ]
Spoiler: OA

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If the area of the square inscribed in the circle shown above is 36  [#permalink]

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New post 06 Sep 2018, 00:13
Bunuel wrote:
Image
If the area of the square inscribed in the circle shown above is 36, what is the area of the circle?


A. \(9\pi\)

B. \(18\pi\)

C. \(\sqrt{72} \pi\)

D. \(4\sqrt{18} \pi\)

E. \(36\pi\)

Spoiler: ::
Attachment:
image009.jpg



side of the square = 6
diagonal of the square = diameter of the circle = a\(\sqrt{2}\) = 6\(\sqrt{2}\)
area of the circle = \(\pi\) 3\(\sqrt{2}\)*3\(\sqrt{2}\) = 18\(\pi\)
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If the area of the square inscribed in the circle shown above is 36  [#permalink]

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New post 06 Sep 2018, 02:23
+1 for B.

Area of Square = S^2 = 36 --> S = 6
Diagonal of Circle = 6√2 (Applying Pythagoras Theorem) , and Radius = 3√2 (Half a diagonal)
Therefore, Area of the circle = πr^2 = π * (3√2)^2 = π * 9 * 2 = 18π

Hence, B.
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Re: If the area of the square inscribed in the circle shown above is 36  [#permalink]

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New post 06 Sep 2018, 06:57
Bunuel wrote:
Image
If the area of the square inscribed in the circle shown above is 36, what is the area of the circle?


A. \(9\pi\)

B. \(18\pi\)

C. \(\sqrt{72} \pi\)

D. \(4\sqrt{18} \pi\)

E. \(36\pi\)

Spoiler: ::
Attachment:
The attachment image009.jpg is no longer available


Diameter of the Circle is \(6√2\) , Hence Raidus of the Circle is \(3√2\)

So, Area of the circle is \(π*3√2*3√2 = 18π\), Answer must be (B)
Attachments

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image001 %281%29.jpg [ 4.71 KiB | Viewed 325 times ]


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