If the ratio of the area of two circles 4:1 what is the ratio of the circumference?
A. 16:1
B. 8:1
C. 4:1
D. 2:1
E. Can't be determine
ans :d
A. 16:1
B. 8:1
C. 4:1
D. 2:1
E. Can't be determine
ans :d
Here are two ways to think about it:
1. Let circle 1 have a radius of a, let circle 2 have a radius of b. if ratio of the areas is 4:1, then Pi*a^2/Pi*b^2=4/1 or a^2/b^2=4 or, taking the square root of both sides, a/b=2. But this turns out to be exactly what we're looking for. The ratio of the circumferences is (2*pi*a)/(2*pi*b)=a/b after cancellations. But we already know a/b=2, so the ratio of the circumferences must be 2:1
2. When two figures are similar (and all circles are similar to each other), the ratio of their areas is always the square of the ratio of their perimeters. And the circumference of a circle is essentially its perimeter. So if the ratio of the areas is 4:1 , the ratio of the circumferences must be the square root of that, or 2:1. I can elaborate more on why this is true if you're interested.
