# What is the circumference of a 15-inch circle if the diameter of a circle is directly proportional to its radius and a circle with a 2-inch diameter has a circumference of approximately 6.28 inches?

I believe the first part of the question was supposed to say that the circumference of a circle is directly proportional to its diameter. That relationship is how we get $\pi$. We know the diameter and the circumference of the smaller circle, $\text{2 in}$ and $\text{6.28 in}$ respectively. In order to determine the proportion between the circumference and diameter, we divide the circumference by the diameter, $\text{6.28 in"/"2 in}$ = $\text{3.14}$, which looks a lot like $\pi$. Now that we know the proportion, we can multiply the diameter of the larger circle times the proportion to calculate the circumference of the circle. $\text{15 in}$ x $\text{3.14}$ = $\text{47.1 in}$.
This corresponds to the formulas for determining the circumference of a circle, which are $C$ = $\pi$$d$ and $2$$\pi$$r$, in which C is circumference, d is diameter, r is radius, and $\pi$ is pi .