What is the formula for the area of a circle?

The formula for the area of a circle is A = πR², where "A" represents the area, "π" is a mathematical constant approximately equal to 3.14159, and "R" is the radius of the circle. This formula arises from the relationship between the radius of the circle and the space enclosed by its boundary.

The reason this formula works is that it calculates how much space is contained within the circle by multiplying the square of the radius by π. The radius is the distance from the center of the circle to any point on its edge, and squaring this value gives a measure of the area as it relates to the circle's dimensions.

All other options are related to circles but define different aspects. For example, one option (A = 2πR) is the formula for the circumference of a circle, which measures the distance around the circle. Another option (A = πd) uses the diameter (d), which is twice the radius, but still does not directly represent the area in its simplest and most intuitive form as A = πR² does. The option that states A = 4πR² refers to the surface area of a sphere, not a circle, further confirming that the