Circle X has an area of 36pie, and a circle Y has an area of 18pie. What is the ratio of the circumference of X to the circumference of Y.
radius of first circle:
πr^2 = 36π
r^2 = 36
r = 6
radius of 2nd circle
πR^2 = 18π
R^2 = 18
R = √18 = 3√2
circum of first = 2π(6) = 12π
circum of 2nd = 2π(3√2) = 6√2 π
ratio of their circumference = 12π : 6√2 π
= 2 : √2
short way:
since the areas vary as the square of their circumferences
ratio of their circumference
= √(36π) / √(18π)
= 6√π : 3√(2π)
= 6:3√2
= 2:√2