Question

If the scale factor between two circles is mc025-1.jpg, what is the ratio of their areas?

Answer 1

Two circles with radii r and R.
The ratio of the radii is R/r
Now let's find the areas.
\(A_r = \pi r^2\) and \(A_R = \pi R^2\)
The ratio of the areas is: \(\dfrac{\pi R^2}{\pi r^2} = \dfrac{R^2}{r^2} = \left(\dfrac{R}{r}\right)^2\)

Answer 2

The conclusion is that the ratio of the areas is the square of the ratio of the radii.