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 OA is C.
I don't have clear this PS question but I have an idea about how to solve it,
I can say that the area of the larger circle is,
$$A_{Lc}=\pi\cdot R^2$$
And the area of the smaller circle is,
$$A_{Sc}=\pi\cdot r^2$$
Also I know that the area of the shaded region is 3 times the area of the smaller circle, then
$$\pi\cdot R^2-\pi\cdot r^2=3\cdot\pi\cdot r^2$$
Now, I can get the difference between the smaller and larger radius, right?
$$\pi\cdot R^2=4\cdot\pi\cdot r^2\ then\ R^2=4\cdot r^2\ finally\ \frac{R}{r}=2$$
That's mean that the circumference of the larger circle is twice than the circumference of the smaller circle, right?
I appreciate if any expert explain it for me. Thank you so much.
