word problem involving circles

Question

The ratio of the circumferences of 2 circles is 3:1. Determine the ratio of the areas of the 2 circles.

Answer 1

All circles are similar. In this case, the scale factor (k) is 3. For any two similar figures (no matter the shape), the ratio of the areas is k². So the ratio of the areas of the two circles is 3² = 9.