Ohio Assessments for Educators (OAE) Mathematics Practice Exam

How is the circumference of a circle calculated?

1. C=πd

2. C=2πr

3. C=πr²

4. C=4r

The correct answer is: C=2πr

The circumference of a circle is calculated using specific mathematical formulas that derive from its geometric properties. The formula represented by the correct answer, C = 2πr, is derived from the relationship between the radius of the circle and its circumference. In this equation, 'C' stands for the circumference, 'r' stands for the radius (the distance from the center of the circle to any point on its boundary), and 'π' (pi) is a constant approximately equal to 3.14159. The factor of 2 in the formula reflects that the diameter of the circle, which is twice the radius (d = 2r), can also be used to calculate the circumference. Hence, the circumference can alternatively be expressed as C = πd. This formula is crucial in various applications, including physics, engineering, and real-life scenarios such as measuring circular objects. Understanding this relationship helps solidify the foundational concepts of geometry, particularly when working with circles. The other options reference related but distinct properties. The formula C = πd is actually another valid expression for circumference, but since it uses diameter instead of radius, that distinction sets it apart. The formula C = πr² pertains to the area of a circle, not