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

The formula for calculating the area of a circle is π multiplied by the square of the radius. This relationship arises from the definition of a circle, where the area represents the space contained within its boundary. In mathematical terms, the area ( A ) can be calculated as ( A = πr² ), where ( r ) denotes the radius. This formula incorporates the constant π (approximately 3.14159) which embodies the ratio of the circumference of a circle to its diameter. By squaring the radius, the formula considers every point within the circular boundary, effectively summing all the infinitesimal contributions across the area.

In contrast, the other options address different concepts. The first option refers to the formula for the circumference, not the area. The second option is another way to express circumference as it utilizes the diameter. Lastly, the fourth choice involves the dimensions typically used for calculating the volume of a cylinder rather than the area of a circle. Understanding these distinctions helps clarify why π × Radius² is the correct and exclusive formula for determining the area of a circle.