How do you determine the area of a circular surface?

The correct formula for determining the area of a circular surface is A = πr². This formula arises from the concept of using the radius of the circle, which is the distance from the center of the circle to any point on its perimeter.

In the formula, "A" represents the area, "π" (pi) is a mathematical constant approximately equal to 3.14159, and "r" is the radius of the circle. By squaring the radius (r²), we account for the dimensions of the two-dimensional space within the circular boundary. It effectively scales the radius in both dimensions — length and width — to provide a measurement of the total area contained within the circle.

This formula is fundamental in geometry and plays a critical role in a wide range of practical applications, from determining the size of land plots and the area of circular tanks to more complex physics and engineering scenarios.

Other formulas listed do not represent the area of a circle. For example, the formula A = 2πr gives the circumference (the perimeter) of a circle rather than its area. Similarly, A = r × Diameter is not valid since it mixes different geometric elements. The equation A = π × Circumference also leads to confusion