What is the formula for the area of a circle?

The formula for the area of a circle is πr², where "r" represents the radius of the circle. This formula arises from the fundamental properties of circles and their geometric relationships. When calculating the area, π (pi) serves as a constant that approximates to 3.14, representing the ratio of the circumference of a circle to its diameter.

Understanding the components of this formula is crucial: the radius is the distance from the center of the circle to its edge, and squaring the radius (multiplying it by itself) allows for the proper scaling required to express the area, which is a two-dimensional measurement.

In contrast, the other choices represent different circle-related calculations. For instance, 2πr calculates the circumference, which is the total distance around the circle, while πd expresses the circumference in terms of diameter instead of radius. Lastly, πr merely conveys a linear measure related to the circle but does not compute area. Recognizing these distinctions reinforces why πr² is the correct formula for determining the area of a circle.