Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What is the formula for the area of a circle?

1. A=2πr

2. A=πr²

3. A=πd

4. A=4πr

The correct answer is: A=πr²

The formula for the area of a circle is A = πr², which indicates that the area (A) is equal to pi (π) multiplied by the radius (r) squared. This relationship is derived from the definition of a circle and the concept of area in geometry. The radius is the distance from the center of the circle to any point on its circumference. When you square the radius and then multiply by π, you establish the total space within the boundaries of the circle. Understanding the significance of π, approximately 3.14, is crucial, as it is the constant that relates the circumference of the circle to its diameter. The squared radius reflects how the area grows exponentially as the circle increases in size, highlighting the importance of understanding dimensions in geometry. In contrast, the other options showcase different mathematical relationships: - The first choice, A = 2πr, represents the circumference of the circle, not its area. - The third option, A = πd, relates to the circumference as well but uses the diameter (d) instead of the radius, and it's less commonly used when discussing area. - Lastly, A = 4πr is not applicable in this context, as it incorrectly suggests a linear relationship that does