To find the area of a circle, what formula is used?

The formula for finding the area of a circle is given by A = πr², where A represents the area and r represents the radius of the circle. This mathematical expression arises from the relationship between the radius and the area encompassed by the circle.

In this formula, π (pi) is a constant approximately equal to 3.14159, which is the ratio of the circumference of any circle to its diameter. When the radius (half of the diameter) is squared, it reflects how the area grows exponentially with increases in the radius. Thus, the area of the circle increases with the square of its radius, showcasing the two-dimensional nature of area measurement.

The other formulas provided correspond to different calculations:

• A = 2πr is actually the formula for the circumference of a circle, not the area.
• A = 4πr refers to the surface area of a sphere with radius r, further deviating from the concept of a two-dimensional area.
• A = πd uses the diameter of the circle, which is related but not the standard way to express area.

By using the correct formula, one ensures accurate calculation of the area, essential for various applications in geometry, physics, and engineering.