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

The formula for calculating the area of a circle is given by πr². In this formula, "π" (pi) is a mathematical constant approximately equal to 3.14159, and "r" represents the radius of the circle, which is the distance from the center of the circle to any point on its boundary.

To understand why this formula works, consider that the area of a circle can be thought of as the result of summing up an infinite number of infinitesimally small concentric rings, or circles, from the center outwards. Each of these rings has a very small thickness, and its area can be approximated as the circumference of that circle (which is 2πr) multiplied by its small thickness. As you integrate these infinitesimal areas from the center of the circle out to the edge, you arrive at the formula πr².

This formula is widely used in various fields, including geometry, physics, and engineering, and is fundamental to understanding shapes and figures in mathematics. The other choices presented serve different geometric purposes: the circumference of a circle is calculated by 2πr, while πd relates to the diameter of the circle. Thus, while they are associated with circles, they