What is the area formula for a circle?

The area of a circle is calculated using the formula that involves the radius squared, specifically π times the radius squared. This is expressed mathematically as A = πr², where A represents the area and r represents the radius of the circle.

The reason this formula works is due to the relationship between the radius and the entire area enclosed by the circle. When you square the radius, you are considering the space within the circle that expands as the radius increases. The π constant represents the ratio of the circumference of a circle to its diameter, and it plays a crucial role in relating the linear dimensions of the circle (such as radius) to its two-dimensional area.

Other formulas mentioned relate to different aspects of a circle. For instance, the formula involving the diameter, while relevant, would not yield the correct area. Similarly, the formula that is simply π times the radius represents the circumference, not the area. The formula with 2 times π times the radius corresponds to the circle's circumference, which is the perimeter length rather than the area.