What is the formula for the area of a circle?

The formula for the area of a circle is derived from its geometric properties. It states that the area (A) is equal to π times the radius (r) squared, which is represented as A = πr². This reflects how the area is related to the radius; as the radius increases, the area grows exponentially since it is squared.

The presence of π in the formula accounts for the circle's constant ratio of circumference to diameter, which is approximately 3.14. This means that if you know the radius of a circle, you can calculate the area by squaring that radius and then multiplying by π. Understanding this relationship is fundamental in many areas of mathematics and physics, as it allows for calculations related to circles in various applications.

The other options provided do not correctly represent the relationship between radius and area for a circle, which is why the answer A = πr² is the only correct choice.