Find the ratio of the circumference of two circles if the radius of one of them is 1/3 of the diameter of the second.

Let’s denote by r the radius of the first circle.

Let us express the radius of the second circle in terms of r.

In the initial data for this task, it is reported that the radius of the first circle is one third of the diameter of the other circle.

Consequently, the diameter of the other circle is three times the radius of the first circle and is 3r.

Since the radius of any circle is half the diameter of that circle, the radius of the second circle is 3r / 2.

Find the circumference l1 of circle number one:

l1 = 2πr.

Find the circumference l2 of circle number two:

l2 = 2π * 3r / 2 = 3πr.

Find the desired ratio of the lengths of the circles:

l1 / l2 = 2πr / (3πr) = 2/3.

Answer: 2/3.