Which formula represents the area of a circle?

The formula for the area of a circle is represented by πr², where r stands for the radius of the circle. This formula arises from the geometric properties of circles and involves squaring the radius (multiplying the radius by itself) and then multiplying by π, which is a constant approximately equal to 3.14. This constant represents the ratio of the circumference of any circle to its diameter.

The area of a circle is essentially a measure of the space contained within the circle itself, and the reasoning behind the formula stems from the accumulation of infinitesimally small sectors that together fill the circle. Thus, the correct representation of this area is vital in both geometry and practical applications such as calculating land area, designing circular objects, and understanding concepts in engineering and physics.