Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

Which formula represents the circumference of a circle?

1. 2πr

2. πr²

3. r²

4. 4πr

The correct answer is: 2πr

The formula for the circumference of a circle is indeed represented by 2πr, where "r" is the radius of the circle. This formula comes from the definition of the circumference, which is the distance around the circle. When you calculate the circumference, you are effectively measuring how far it would be to walk around the edge of the circle. The factor of 2 comes from the fact that the circumference is twice the radius multiplied by π (pi), which is a constant that represents the ratio of a circle's circumference to its diameter. The other options present different formulas related to circles but serve different purposes. For instance, πr² represents the area of a circle, which is the amount of space enclosed within the circle itself. The term r² alone does not relate directly to the circumference or any circular dimension, as it simply represents the square of the radius. Finally, the formula 4πr does not represent a standard geometric measurement for circles but instead might be related to other shapes or contexts, such as the surface area of a sphere when further modified. Thus, the formula for circumference, 2πr, is the appropriate choice for understanding the distance around a circle.