What is the formula for calculating the area of a circle?

The formula for calculating the area of a circle is indeed represented by A = πr², where A stands for the area and r represents the radius of the circle. This relationship arises from the definition of area in a geometric context and is derived from the constant ratio of the circumference to the diameter of a circle, known as π (pi).

In this formula, when you square the radius (r²), you account for the two-dimensional nature of the area, effectively multiplying the radius by itself to cover the entire circular space. It's crucial to note that the area increases with the square of the radius, which means that even a small increase in radius leads to a significantly larger area, demonstrating the exponential growth of the circle’s area relative to its radius.

The other options do not accurately represent the area of a circle. While they may represent other geometric relationships or formulas, they fail to encapsulate the specific mathematical relationship that defines the area of a circle in terms of its radius. Thus, A = πr² is the only correct and standardized formula for this calculation.