Ohio Assessments for Educators (OAE) Mathematics Practice Exam 2025 - Free Practice Questions and Study Guide

The formula for calculating the area of a circle is derived from the relationship between the radius and its dimensions. Specifically, the area (A) is determined using the radius (r), which is the distance from the center of the circle to its edge. The correct formula is A = πr², where π (pi) is a constant approximately equal to 3.14159.

This formula captures how the area increases as the radius increases, since the radius is squared in the equation. Squaring the radius signifies that the area is not linear but rather proportional to the square of the radius, meaning a slight increase in the radius results in a significantly larger area.

The other options present incorrect formulas: the second option relates to the circumference of a circle, which measures its perimeter rather than its area. The third and fourth options provide incorrect formulations that do not accurately represent the relationship needed to derive the area based on the radius. Therefore, the choice of A = πr² is foundational in geometry and essential for understanding circle measurements.