The circumference $C$ of a circle is proportional to the diameter $d$, and we can write this relationship as $C = \pi d$. The circumference is also proportional to the radius of the circle, and the constant of proportionality is $2 \boldcdot \pi$ because the diameter is twice as long as the radius. However, the area of a circle is not proportional to the diameter (or the radius). 

The area of a circle with radius $r$ is a little more than 3 times the area of a square with side $r$ so the area of a circle of radius $r$ is approximately $3r^2$. We saw earlier that the circumference of a circle of radius $r$ is $2\pi r$. If we write $C$ for the circumference of a circle, this proportional relationship can be written $C = 2\pi r$.

The area $A$ of a circle with radius $r$ is approximately $3r^2$.  Unlike the circumference, the area is not proportional to the radius because $3r^2$ cannot be written in the form $kr$ for a number $k$. We will investigate and refine the relationship between the area and the radius of a circle in future lessons.