How is the area of a circle calculated?

The area of a circle is calculated using the formula A = πr², where A represents the area and r represents the radius of the circle. This formula arises from integral calculus and geometry, effectively summing up an infinite number of infinitesimally small wedges that make up the circle.

The π (pi) in the formula reflects the constant ratio of the circumference of any circle to its diameter, which is approximately 3.14159. Since the area is directly proportional to the square of the radius, if the radius increases, the area increases by the square of that increase, demonstrating the relationship between these quantities.

This choice accurately encapsulates the method for determining the area inside the boundaries of a circle, allowing for mathematical calculations relating to circles in various applications, such as engineering, architecture, and physical sciences. Other formulas provided do not represent the area but may describe other aspects of the circle, such as its circumference or dimensions.