What is the area of a circle expressed in terms of radius?

The area of a circle is determined using the formula A = πr², where A represents the area and r is the radius of the circle. This formula arises from the relationship between the radius and the space contained within the circle.

In this context, π (pi) is a constant approximately equal to 3.14, and it represents the ratio of the circumference of any circle to its diameter. The radius, which is the distance from the center of the circle to its edge, plays a critical role in this formula because the area is directly proportional to the square of the radius. Thus, as the radius increases, the area grows exponentially since it is squared.

For example, if the radius were doubled, the area would increase by a factor of four, highlighting how the area relates to the radius through this quadratic relationship. This makes the formula πr² essential for calculating the area of a circle based on its radius.

The other options, while they may involve π and r, do not represent the area of a circle accurately. This makes the choice of πr² the clear and correct expression for the area of a circle in terms of its radius.