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Geometry

by Deepthi Subbu » Thu Nov 11, 2010 9:10 am
I am not sure about adding an image here.But here is the description . There is a square thats circumscribed by a circle(a square inside a circle) .

Q : Area of the square is 16 . What is the area of the circle?

a. 8 pie
b. 4 pie
c. 2 pie
d. pie
e. pie + 2































































































[/img]
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by goyalsau » Thu Nov 11, 2010 9:19 am
Deepthi Subbu wrote:I am not sure about adding an image here.But here is the description . There is a square thats circumscribed by a circle(a square inside a circle) .

Q : Area of the square is 16 . What is the area of the circle?

a. 8 pie
b. 4 pie
c. 2 pie
d. pie
e. pie + 2

[/img]
Where is the image......??????????????????
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by limestone » Thu Nov 11, 2010 9:37 am
Hi,

I cant see the picture. However, as far as I understand, the diagonal of the square is the diameter of the circle.

The square area = 16, thus the length of its side is 4, and the length of its diagonal is 4*sqrt2.

Thus the radius of the circle is half its diameter, or half the length of the square's diagonal:
=(4*sqrt2)/2 = 2*sqrt(2).

The area of the circle is:
= r^2*Pi = (2*sqrt2)^2*Pi = 8*Pi

Thus A should be the answer.
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by Deepthi Subbu » Thu Nov 11, 2010 10:00 am
Hello limestone ,

You got the right answer . But how are u considering the diagonal to be the diameter of the circle??
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square.png
here is the image that I was talking about
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by MAAJ » Thu Nov 11, 2010 10:55 am
Because it's a square we know that if we cut the square in half we get a right triangle which sizes will be proportional in scale of 1:1:sqrt(2) (the sqrt(2) is for the side facing the 90 angle).

Knowing this we can determine that the diagonal of the square is 4*sqrt(2) which is the Diameter of the circle. So the radius is 2*sqrt(2). Now that we know the radius we can determine the area of the circle:

(2*sqrt(2))^2 * pie
2^2 * (sqrt(2))^2 * pie
4 * 2 * pie
8 pie

Correct Answer: [spoiler](A)[/spoiler]

PS: If you are having a hard time with triangles you can get some help from the top 7 triangle tricks https://www.beatthegmat.com/mba/2009/10/ ... art-1-of-7. Hope it helps!!!
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by Deepthi Subbu » Thu Nov 11, 2010 11:52 am
Thanks a lot for the link on triangle tricks . That really helped :)
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by MAAJ » Thu Nov 11, 2010 12:15 pm
Deepthi Subbu wrote:Thanks a lot for the link on triangle tricks . That really helped :)
No problem :)!!!
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