If the radius of the small circle is 1/3 the radius of the big circle, how do their areas compare

The big circle has 9 times the area of the smaller circle.

Step-by-step explanation:

We can set up a proportion, where r is the radius of the big circle. That means the smaller circle would have a radius of r/3. By the area formula for a circle we know that A=πr², so the radius for both would be squared, which gives us r² for the big one and r²/9 for the smaller one. It then becomes clear that the ratio between the two areas is 9 times.