What is the formula for finding the area of a circle?

The formula for finding the area of a circle is based on the relationship between the radius and the constant π (pi). The area of a circle is calculated using the formula π x radius². This is derived from the definition of the circle itself, which states that the area is proportional to the square of the radius. Because π (approximately 3.14) represents the relationship between the circumference and the diameter of the circle, using the radius in this formula provides an accurate measurement of the space contained within the boundaries of the circle.

In contrast, the other options do not correctly describe the area. The formula involving the diameter squared mistakenly applies the diameter when the area depends on the radius; although the diameter is twice the radius, squaring it does not result in the same area calculation. The options involving 2π (i.e., calculating circumference) are even more different, as they relate to the measurement around the circle rather than the space it fills. Thus, using the correct area formula captures the essential relationship between the radius and the area of a circle.