If the radius of one circle is 6 times the radius of another, what is the ratio of their areas? Of their circumferences? Of their diameters?

Question

The answers that I got are 36:1 (as areas), 6:1 (as circumferences), and 6:1 (as diameters), but the teacher puts the answers as 1:36, 1:6, and 1:6. Can both of the ways be correct? I mean the question does not say which radius comes first...so that’s why I put the radius with 6 times greater first. Please help.

Answer 1

Areas:

π(6r)² / πr² = 36

Circumferences:

2π(6r) / 2πr = 6

Diameters:

2(6r) / 2r = 6

Your answers are correct. What your teacher did was divide the smaller by the larger, which inverts the ratios. That is correct too, as long as it is made clear which one is divided by the other.