Mathematics ACT Aspire Test 2025 – 400 Free Practice Questions to Pass the Exam

The formula for the area of a circle is given by πr², where r represents the radius of the circle. This formula arises from the relationship between the radius and the circular shape.

To understand this, consider that the area of a circle can be visualized as the total space enclosed within the boundary of the circle. The factor π (pi) is a mathematical constant approximately equal to 3.14159, which relates the circumference of any circle to its diameter. When you square the radius (r²), you are essentially scaling the space as you account for the entirety of the circle from the center outwards.

Each tiny segment of the circle can be thought of as contributing an area that collectively adds up to the total area defined by the radius. Doubling the radius (to calculate area) results in quadrupling the area since the area grows with the square of the radius.

In contrast, other options refer to either the circumference, which is the total distance around the circle, or incorrect expressions that do not represent the area. Thus, choosing the formula πr² accurately captures the relationship of the radius of a circle to the area it encloses.