Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

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What is the formula for calculating the circumference of a circle?

Circumference = π * diameter
Circumference = 2π * radius
Circumference = radius * 2 + diameter
Circumference = π * radius²

The correct answer is: Circumference = 2π * radius

The formula for calculating the circumference of a circle is rooted in the relationship between the circle's radius and its diameter. One of the most fundamental ways to express this relationship is through the diameter, which is twice the radius. Therefore, when we consider the formula for circumference in terms of the radius, it is derived from the connection that the circumference equals 2 times the radius multiplied by π, also expressed as 2π * radius. This correct approach uses the radius, which is often more convenient, especially when the radius is known. In contrast, other options provide forms that either misstate the relationships or mix terms inappropriately. For example, while one option mistakenly introduces the diameter alongside an incorrect addition, another incorrectly suggests multiplying the radius by π in a way that does not accurately convey the relationship needed to find circumference. This clarity in the relationship to circumference emphasizes why referencing the radius and including the appropriate multiplication by 2 and π is essential.