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

The formula for calculating the area of a circle is A = πr², where A represents the area and r is the radius of the circle. This formula is derived from the relationship between the radius and the curve of the circle. The constant π (pi) is approximately 3.14159 and represents the ratio of the circumference of any circle to its diameter. By squaring the radius (r²), the formula accounts for the size of the circle in two dimensions, effectively measuring the total space inside the boundary of the circle.

Using this formula correctly allows one to determine the area of any circle, which is crucial in various applications in geometry and real-world problem-solving, such as calculating the amount of materials needed to cover a circular surface. The other options reflect different formulas that do not fit the definition of area: 2πr relates to the circumference, πd also relates to circumference, and r²/π does not represent a valid geometric interpretation for the area of a circle.