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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, 00:15
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35% (medium)

Question Stats:

74% (01:52) correct 26% (02:32) wrong based on 106 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 1057 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, 02:07
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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, 03:02
+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, 06:38
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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 860 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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The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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20 Oct 2018, 23:17
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

Area of Circle is 32

A. $$\frac{8}{\pi}$$ : approx 3 unit

B. $$\frac{8\sqrt{2}}{\pi}$$ : approx 4 units

C. $$\frac{32}{\pi}$$ : around 10 or 11

D. $$\frac{64}{\pi}$$ : approx 22

E. 32 : not possible

Only seems to be a correct choice..

sometimes we can save a lot of time just by using simple ways.. ONLY SOMETIMES..
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The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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21 Oct 2018, 01:46
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

Formula used to calculate the area of circumscribed square $$2*r^2$$ where r is radius of circle

Dagonal of square is equal to diameter of circle

Area of Circle $$\pi*r^2$$ =$$32$$

Taking square root on both sides
$$\sqrt{\pi*r^2}$$ = $$\sqrt{32}$$

i.e $${\sqrt{\pi}}*r$$= $$\sqrt{16*2}$$

i.e $${\sqrt{\pi}}*r$$= $$4\sqrt{2}$$

so r = $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$

2 * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ = $$\frac{2 *32}{\pi}$$ = $$\frac{64}{\pi}$$

Bunuel pushpitkc can you pls format my explanation - (the square roots/ radicals/ fractions in a math friendly way

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

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21 Oct 2018, 03:41
1
dave13 wrote:
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

Formula used to calculate the area of circumscribed square $$2*r^2$$ where r is radius of circle

Dagonal of square is equal to diameter of circle

Area of Circle $$\pi*r^2$$ =$$32$$

Taking square root on both sides
$$\sqrt{\pi*r^2}$$ = $$\sqrt{32}$$

i.e $${\sqrt{\pi}}*r$$= $$\sqrt{16*2}$$

i.e $${\sqrt{\pi}}*r$$= $$4\sqrt{2}$$

so r = $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$

2 * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ * $$\frac{4\sqrt{2}}{\sqrt{\pi}}$$ = $$\frac{2 *32}{\pi}$$ = $$\frac{64}{\pi}$$

Bunuel pushpitkc can you pls format my explanation - (the square roots/ radicals/ fractions in a math friendly way

thank you

dave13 - Indeed, a nice way to solve the problem. Edited your solution
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Re: The area of the circumscribed circle in the figure above is 32. What  [#permalink]

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15 Nov 2018, 16:06
GMATinsight wrote:
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

Im having immense difficulty with this question. I follow up to this point

i.e. a√2 = 2*√(32/π)

i.e. a = 8/√π

How did you arrive at 8/√π ?

Your help would be greatly appreciated!
Re: The area of the circumscribed circle in the figure above is 32. What   [#permalink] 15 Nov 2018, 16:06
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