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555-605 (Medium)|   Geometry|      
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Bunuel
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The area of the circumscribed circle in the figure above is 32. What 06 Sep 2018, 01:15
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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


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D
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The area of the circumscribed circle in the figure above is 32. What 06 Sep 2018, 03:07
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Bunuel


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


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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

Answer: Option D
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The area of the circumscribed circle in the figure above is 32. What 06 Sep 2018, 04:02
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+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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The area of the circumscribed circle in the figure above is 32. What 06 Sep 2018, 07:38
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Bunuel


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


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image001 %281%29.jpg [ 5.83 KiB | Viewed 2926 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 21 Oct 2018, 00:17
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Bunuel


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

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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 21 Oct 2018, 02:46
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Bunuel


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


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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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The area of the circumscribed circle in the figure above is 32. What 21 Oct 2018, 04:41
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dave13
Bunuel


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


Show Spoiler
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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dave13 - Indeed, a nice way to solve the problem. Edited your solution :)
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The area of the circumscribed circle in the figure above is 32. What 15 Nov 2018, 17:06
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Bunuel


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


Show Spoiler
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

Answer: Option D
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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!
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