Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is the formula for the area of a circle?

1. 2πr

2. πd

3. πr²

4. 4r

The correct answer is: πr²

The formula for the area of a circle is expressed as πr², where "π" (pi) is a constant approximately equal to 3.14, and "r" represents the radius of the circle. This formula is derived from the concept of calculating the space enclosed within the circular boundary. To understand why this formula works, consider that the area can be thought of as the total number of unit squares that can fit inside the circle. The radius serves as the distance from the center of the circle to its edge, effectively determining the size of the circle. By squaring the radius, you essentially scale the area proportionally to the radius itself. The factor of π is essential because it relates the linear dimensions to the non-linear shape of the circle, effectively translating the radius into a measure of area. In contrast, other options represent different geometric concepts. For example, 2πr calculates the circumference of a circle, which is the total distance around it, while πd represents the same circumference but in terms of diameter instead of radius. The choice of "4r" does not apply to the area of a circle at all; instead, it might represent the perimeter of a square with each side measuring "r". Thus,