What is the formula for the area of a circle?

The formula for the area of a circle is given by A = πr². This formula arises from the relationship between the radius of the circle and the constant π (pi), which is approximately 3.14.

In this formula, "A" represents the area of the circle, "r" is the radius, which is the distance from the center of the circle to any point on its circumference. When you square the radius (r²) and multiply it by π, you effectively capture the entire space contained within the circle.

Understanding this formula is key for geometric calculations involving circles, including real-world applications like determining the size of round surfaces or objects. It demonstrates how the area grows with respect to the radius; increasing the radius will significantly increase the area since it is squared.

The other choices do not represent the correct formula for the area of a circle. For instance, A = πd involves the diameter but does not give an area measurement, while A = 2πr describes the circumference of a circle, and A = r² + h² is related to the Pythagorean theorem, which applies to right triangles, not circles. Thus, C is indeed the correct choice for the area of a circle.