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Master | Next Rank: 500 Posts
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by smclean23 » Mon Aug 04, 2008 10:32 am
Let S be the length of the side of a square inscribed in a circle of radius R. Which of the following represents the ratio of the area of the circle to that of the square?

Pi/2
2r
Pi(r)
4Pi(r^2)
8Pi(r^2)

What is the methodology?



A
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by eccentric » Mon Aug 04, 2008 10:42 am
The square inscribed in a circle has diagonal as diameter of circle.
The half of square makes a 45-45-90 triangle
with hyp as 2R
thus (2R)^2 = x^2+x^2 = 2x^2 area of square is 2R^2
and area of circle is pi R^2
thus ratio of area of circle to area of square is pi/2
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Another way to look at it

by Gaurav Tyagi » Mon Aug 04, 2008 12:21 pm
A first look at this problem gives me an idea that any answer to this problem cannot contain any variable R or S as it is asking for a ratio of squares in which either both R and S should be there in the answer or none of them. Hence, I can eliminate b,c,d and e.
Thanks,

GT
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by smclean23 » Mon Aug 04, 2008 4:43 pm
I got everything you said except how u got the hyp as 2R and the area of the circle being 2R^2.....thanks in advance for the help
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by sibbineni » Mon Aug 04, 2008 5:11 pm
how u got the hyp as 2R

since in question it is given the radius=R

here diameter=2*R

so hypotenuse-->2R

u mean area of square....

side^2
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