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

The formula for calculating the area of a circle is derived from its relationship between the radius and the dimensions of a circle. In this case, the correct answer indicates that the area is calculated using the formula Area = π × r², where r represents the radius of the circle.

This formula signifies that the area of the circle is directly proportional to the square of its radius, multiplied by the constant π (approximately 3.14159). This relationship stems from the geometric principles of circles, where the area can be understood as the space contained within the boundary of the circle.

The other choices provide formulas that either represent different geometric concepts or incorporate incorrect relationships. For instance, the formula that involves multiplying the radius by 2π only gives the circumference of the circle, not the area. Similarly, the formula using the diameter highlights another relationship in circles but does not directly reflect the area as required. The option suggesting area equals r² divided by π does not align with geometric principles related to the area of a circle, as it lacks the correct proportional relationship involving the square of the radius.

Understanding this formula is fundamental in physics, engineering, and various mathematical applications where circular shapes are prevalent.