Hi,
I dont have OA but hope someone could help
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Answer is 2.
Just plug the equations in assuming the bigger circle is of radius R and the smaller circle is of radius r. you will get the answer.
Calista.
Just plug the equations in assuming the bigger circle is of radius R and the smaller circle is of radius r. you will get the answer.
Calista.

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Sorry StarDust845! I cann't be agree with u. According to me,
Let R = radius of large circle
r = radius of small circle
Now 3 * pi * r^2 = pi * (R  r)^2
So (R  r) = sqrt(3) * r
Now circumference of big circle : circum of small circle = 2 * pi * (R  r) / 2 * pi * r = (R  r) / r = sqrt(3).
So IMO D
Let R = radius of large circle
r = radius of small circle
Now 3 * pi * r^2 = pi * (R  r)^2
So (R  r) = sqrt(3) * r
Now circumference of big circle : circum of small circle = 2 * pi * (R  r) / 2 * pi * r = (R  r) / r = sqrt(3).
So IMO D
Correct me If I am wrong
Regards,
Amitava
Regards,
Amitava

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Area of Shaded Region = pi* (R^2  r^2)
Area of Smaller circle = pi*r^2
Hence (R^2  r^2)/r^2 = 3
R/r = sqrt(2)
Area of Smaller circle = pi*r^2
Hence (R^2  r^2)/r^2 = 3
R/r = sqrt(2)

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I am afraid the equiation should be 3*pi*r^2=pi * (R^2r^2), answer should be 2.camitava wrote:Sorry StarDust845! I cann't be agree with u. According to me,
Let R = radius of large circle
r = radius of small circle
Now 3 * pi * r^2 = pi * (R  r)^2
So (R  r) = sqrt(3) * r
Now circumference of big circle : circum of small circle = 2 * pi * (R  r) / 2 * pi * r = (R  r) / r = sqrt(3).
So IMO D
Let R be the radius of bigger circle and r be the radius of the smaller one.
Then
*Note Pi is denoted by #
((#R^2)(#r^2)/(#r^2))=3/1
=> #R^2=4#r^2
=> R=2r
Ratio of Circumference of the two circles is the ratio of the radius
Hence R/r=2 from above.
Correct answer is 2.
Then
*Note Pi is denoted by #
((#R^2)(#r^2)/(#r^2))=3/1
=> #R^2=4#r^2
=> R=2r
Ratio of Circumference of the two circles is the ratio of the radius
Hence R/r=2 from above.
Correct answer is 2.
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how do you get fromAuzbee wrote:Let R be the radius of bigger circle and r be the radius of the smaller one.
Then
*Note Pi is denoted by #
((#R^2)(#r^2)/(#r^2))=3/1
=> #R^2=4#r^2
=> R=2r
Ratio of Circumference of the two circles is the ratio of the radius
Hence R/r=2 from above.
Correct answer is 2.
"((#R^2)(#r^2)/(#r^2))=3/1"
to
"=> #R^2=4#r^2"
???
thanks.
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I am with Auzbee on this. I also think that the answer is 2. Does anyone actually have the official answer:
How I came to the answer, with some help from Auzbee !
Let R = big circle radius
Let r = small circle radius
Big circle area = ∏R²
Small circle area = ∏r²
Shaded area = Big circle area  Small circle area
Shaded area = ∏R²  ∏r²
The question tells us that the shaded area is 3 time the small circle area.
Shaded area = 3 x ∏r²
∏R²  ∏r² = 3(∏r²)
∏R² = 3(∏r²)+(∏r²)
∏R² = 4(∏r²)
Lets get rid of the squares ... so we have to apply √ to both sides of the equation:
√∏R² = √4(∏r²)
∏R = 2∏r
∏R/∏r = 2∏r/∏r
∏R/∏r = 2
Remove ∏ from both numerator and denominator from left hand side:
R/r = 2
So the radius of the big circle (R) is twice as big as the small circle radius (r).
Therefore the circumference will also be twice as big, so the answer is C.
Thanks.
II
How I came to the answer, with some help from Auzbee !
Let R = big circle radius
Let r = small circle radius
Big circle area = ∏R²
Small circle area = ∏r²
Shaded area = Big circle area  Small circle area
Shaded area = ∏R²  ∏r²
The question tells us that the shaded area is 3 time the small circle area.
Shaded area = 3 x ∏r²
∏R²  ∏r² = 3(∏r²)
∏R² = 3(∏r²)+(∏r²)
∏R² = 4(∏r²)
Lets get rid of the squares ... so we have to apply √ to both sides of the equation:
√∏R² = √4(∏r²)
∏R = 2∏r
∏R/∏r = 2∏r/∏r
∏R/∏r = 2
Remove ∏ from both numerator and denominator from left hand side:
R/r = 2
So the radius of the big circle (R) is twice as big as the small circle radius (r).
Therefore the circumference will also be twice as big, so the answer is C.
Thanks.
II

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I should read all the posts before posting mine. Camitava corrected his solution earlier.. so deleting my comments and posting only the solution.
<deleting>
Given: PI (R^2  r^2) = 3PIr^2 which implies (R/r)^2 = 4 and hence R/r = 2
That is what we want. Hence the ratio is 2 that is C in the given choices.
Calista.
<deleting>
Given: PI (R^2  r^2) = 3PIr^2 which implies (R/r)^2 = 4 and hence R/r = 2
That is what we want. Hence the ratio is 2 that is C in the given choices.
Calista.
Last edited by StarDust845 on Sun Jan 06, 2008 12:10 pm, edited 2 times in total.