The formula for calculating the area of a circle is?

The formula for calculating the area of a circle is represented by πr², where "r" stands for the radius of the circle. This formula derives from the fundamental geometric principle that the area of a circle is proportional to the square of its radius. The constant π (pi) represents the ratio of the circumference of the circle to its diameter and is approximately equal to 3.14159.

When you apply this formula, you are essentially determining how much space is contained within the boundary of the circle. By squaring the radius, you account for the two-dimensional nature of the area. Therefore, when you plug in the radius value into the formula, you can effectively calculate the total area enclosed by the circle.

Other options represent different properties related to circles. For instance, 2πr is the formula for the circumference of a circle, relating to the distance around it, while πd refers to the same concept, using the diameter instead of the radius. The choice r² by itself does not include π and does not accurately represent a circle's area without that specific proportionality constant. Thus, using πr² is essential for correctly calculating the area of a circle.