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ratio of geomatry

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by alltimeacheiver » Tue Apr 05, 2011 10:06 pm
If the area of square S and the area of circle C are equal, then the ratio of the perimeter of S to the circumference of C is closest to


I got ans 2/1 straight away. but the ans is 9/8. Is that the case that we need to consider Pie over here. but how
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by HSPA » Tue Apr 05, 2011 10:13 pm
s^2 = pi* r^2 --- stat 1
we need 4s in terms of 2*pi*r

Let us say pi = 3
From stat 1 we have s = sqrt3 * r

perimeter/circumf = 4*sqrt 3/ 6 = 2/sqrt3 = 2/1.7 ~ 2.2
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by vineeshp » Tue Apr 05, 2011 10:16 pm
s^2 = Pi r^2 (s is side of square S, r is radius of the cirlce)
s = Root of (Pi * r^2) = r * Root(Pi)

We need to find ratio of perimeter to circumference.
4s / 2 Pi r
Vineesh,
Just telling you what I know and think. I am not the expert. :)
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by Anurag@Gurome » Tue Apr 05, 2011 10:17 pm
alltimeacheiver wrote:If the area of square S and the area of circle C are equal, then the ratio of the perimeter of S to the circumference of C is closest to


I got ans 2/1 straight away. but the ans is 9/8. Is that the case that we need to consider Pie over here. but how
If s is the side of square, then area of square = s²
If r is the radius of circle, then area of circle = (pi)r²
s² = (pi)r² implies s = r√(pi)
Perimeter of square = 4s = 4r√(pi)
Circumference of circle = 2(pi)r
So, Perimeter of square:Circumference of circle = 4r√(pi):2(pi)r = 2:√(pi) = 2:1.8

Now we need to have the answer choices to answer this question. Can you please post the same?
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by alltimeacheiver » Tue Apr 05, 2011 10:35 pm
A 7/9

B 8/9

C 9/8

D 4/3

E 2/1
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by Anurag@Gurome » Tue Apr 05, 2011 10:37 pm
alltimeacheiver wrote:A 7/9

B 8/9

C 9/8

D 4/3

E 2/1
2:1.8 is closest to 9:8

The correct answer is C.
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by force5 » Wed Apr 06, 2011 12:18 am
hi Anurag.. can you please help us know how did you find out that 2:Sqrtπ was equal to 9/8 and not 4/3. I would have marked D in the exam.approx the value of π to 3.
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