What is the formula to calculate the area of a circle?

The formula to calculate the area of a circle is derived from its geometric properties. The correct formula, which states that the area is equal to π times the radius squared (Area = πr²), applies to any circle. In this formula, π (pi) is a mathematical constant approximately equal to 3.14159, representing the ratio of the circumference of a circle to its diameter. The radius (r) is the distance from the center of the circle to any point on its perimeter.

To understand why this formula is used, consider that the area of a circle is essentially the number of square units that can fit within the boundary of the circle. As the radius increases, the area grows exponentially due to the squaring of the radius in the formula. This relationship shows how critical the radius is in determining the size of the circle.

The other options do not represent the correct area of a circle. For instance, the formula involving only the radius and π without squaring it does not account for the full dimensions of the circular area. Similarly, specific numeric approximations or erroneous divisions involving the radius cannot accurately quantify the area in relation to its geometrical attributes. The primary focus of the correct formula ensures that the relationship between the radius and the