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# The area of the circumscribed circle in the figure above is 32. What

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The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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06 Sep 2018, 01:15
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45% (medium)

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65% (01:34) correct 35% (02:42) wrong based on 19 sessions

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The area of the circumscribed circle in the figure above is 32. What is the area of the square?

A. $$\frac{8}{\pi}$$

B. $$\frac{8\sqrt{2}}{\pi}$$

C. $$\frac{32}{\pi}$$

D. $$\frac{64}{\pi}$$

E. 32

Attachment:

image001 (1).jpg [ 2.78 KiB | Viewed 333 times ]

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The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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06 Sep 2018, 03:07
Bunuel wrote:

The area of the circumscribed circle in the figure above is 32. What is the area of the square?

A. $$\frac{8}{\pi}$$

B. $$\frac{8\sqrt{2}}{\pi}$$

C. $$\frac{32}{\pi}$$

D. $$\frac{64}{\pi}$$

E. 32

Attachment:
image001 (1).jpg

Area of the circle = πr^2 = 32

i.e. r = √(32/π)

Diagonal of the Square = a√2 (where a is the side of square) = Diameter of circle = 2*r

i.e. a√2 = 2*√(32/π)

i.e. a = 8/√π

Area of the square = a^2 = (8/√π)^2 = 64/π

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Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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06 Sep 2018, 04:02
+1 for D.

Area of Circle = π* r^2 = 32, r = √(32/π), and d = 2*√(32/π)
Now, Area of Square = d^2 / 2 = ((4*32) / π) / 2 = 64 / π

Hence, D.
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Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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06 Sep 2018, 07:38
Bunuel wrote:

The area of the circumscribed circle in the figure above is 32. What is the area of the square?

A. $$\frac{8}{\pi}$$

B. $$\frac{8\sqrt{2}}{\pi}$$

C. $$\frac{32}{\pi}$$

D. $$\frac{64}{\pi}$$

E. 32

Attachment:
The attachment image001 (1).jpg is no longer available
Attachment:

image001 %281%29.jpg [ 5.83 KiB | Viewed 182 times ]
So Radius is $$\frac{a√2}{2}$$

Now, Area of the Circle is $$\frac{2a^2π}{4}=32$$

Or, $$a^2π=64$$

Or, $$a^2=\frac{64}{π}$$ = Area of the square , Answer must be (D)
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Re: The area of the circumscribed circle in the figure above is 32. What &nbs [#permalink] 06 Sep 2018, 07:38
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