Sheree, thank you for using the app. In this question, we are not explicitly calculating the areas. Rather we are asked to calculate the ratio of the shaded area and the inner / smaller circle. In this type of problem, it is best to express the calculations using an assumed variable, like x, y, a, b, r. Ready?

Assume the radius of the smaller circle is r, and that of the outer circle is R. The problem tells us that R = 2r. That is, the problem is not telling you the ratio of the circle's areas, just the ratio of the radii.

The area of the shaded region = area of big circle - area of small circle
= πR^2 - πr^2. To calculate the ratio, we need to express the whole thing in r, substituting R with 2r. So,
= π(2r)^2 - πr^2
= π4r^2 - πr^2
= 3πr^2

To compute the ratio, let's divide the area of the shaded region with the area of the small circle, which is πr^2:
3πr^2 : πr^2 = ...