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I know the formula. But could not arrange it properly.
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In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?
A. 4
B. 3
C. 2
D. \sqrt{3}
E. \sqrt{2}

The area of the shaded region is area_{shaded}=\pi{R^2}-\pi{r^2} and the area of the smaller circle is area_{small}=\pi{r^2}. Given: \pi{R^2}-\pi{r^2}=3\pi{r^2} --> R^2=4r^2 --> R=2r;

Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2.

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circular shaded region = area of large circle - area of small circle = 3 * area of small circle
so area of large circle = 4 * area of small circle

that means radius oflarge circle = 2 * radius of small circle
so the cicumference of large circle is 2 times that of the small circle ---Option C
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