What is the formula for the area of a circle?

The formula for the area of a circle is given by the expression A = (\pi r^2), 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 dimensions of the circle.

When calculating the area of a circle, we consider that the area is a measure of the space enclosed within the circle. The constant (\pi) (approximately 3.14159) relates the circumference of the circle to its diameter and plays a crucial role in the formula. By squaring the radius (r^2), we account for the fact that the area increases with the square of the radius, meaning that if the radius doubles, the area increases by a factor of four.

This formula captures the full geometry of a circle, allowing one to determine the area for any circle as long as the radius is known. The other choices do not represent the area; they either represent a linear measure (like the circumference) or introduce incorrect terms that are not applicable to calculating area in relation to a circle.