Two circles have diameters in the ratio1:3. Find the ratio of their circumerences.

Suppose that the radius of circles are: D1 and D2.

We'll express the ratio of the 2 diameters as:

D1/D2=1/3

We know that the diameter of a circle is twice the radius of that circle, so:

 D1/D2=2*R1/ 2*R2=R1/R2=1/3

The formula expressing the length of the circle is 2*pi*R.

The length of the first circle is: 2*pi*R1.

The length of the second circle is: 2*pi*R2.

The ratio of the circumferences of the 2 circles:

2*pi*R1/2*pi*R2

Simplifying constant pi and 2 , we'll get:

2*pi*R1/2*pi*R2=R1/R2

But R1/R2=1/3, as we've demonstrated before, so:

2*pi*R1/2*pi*R2=R1/R2=1/3