Ontario Mathematics Proficiency Practice Test

The circumference of a circle is defined as the distance around the circle, and it can be calculated using two primary formulas that are closely related: Circumference = 2πr and Circumference = πd.

The formula of Circumference = 2πr is derived from the relationship between the radius (r) of the circle and π (pi), which is a constant approximately equal to 3.14. The factor of 2 arises because the circumference spans the distance across the circle from one side to the other and back around. When you multiply the radius by 2, you effectively get the diameter of the circle (d), and multiplying that diameter by π aligns it with the definition of the circle's circumference.

This formula emphasizes the direct relationship that the radius has with the circumference: as the radius increases, the circumference also increases proportionally.

In the other options, some do not represent the properties of a circle accurately, such as the one involving squaring the radius or adding linear dimensions, which are not applicable to calculating circumference. Understanding this primary formula is crucial in solving problems related to circles and helps in grasping more advanced geometric concepts.