What is the relationship between the radius and the circumference of a circle?

The relationship between the radius and the circumference of a circle is directly proportional. This means that as the radius increases, the circumference also increases in a predictable manner. The formula that defines this relationship is given by the equation ( C = 2\pi r ), where ( C ) represents the circumference and ( r ) represents the radius.

In this formula, (\pi) is a constant, which indicates that the circumference increases in a linear fashion with respect to the radius. This constant ratio signifies that for every unit increase in radius, the circumference increases by a factor of ( 2\pi ). Therefore, if you were to double the radius, the circumference would also double, reaffirming the idea of direct proportionality. This clear and consistent connection is crucial in understanding properties of circles in geometry.