Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is the relationship between the diameter and the radius of a circle?

1. The diameter is equal to the radius

2. The diameter is twice the radius

3. The diameter is half the radius

4. The diameter and radius are unrelated

The correct answer is: The diameter is twice the radius

The relationship between the diameter and the radius of a circle is defined by the fundamental geometric properties of a circle. The diameter is the longest distance across the circle, passing through its center, while the radius is the distance from the center of the circle to any point on its perimeter. Mathematically, the diameter is always twice the length of the radius. This can be expressed with the formula: diameter = 2 × radius. Therefore, when comparing these two measures, it is clear that knowing one allows for straightforward calculation of the other. For instance, if the radius of a circle is known to be 5 units, the diameter would be 10 units, demonstrating that the diameter indeed is double the radius. In contrast, the other options misrepresent the relationship. The first option suggests that both measurements are equal, which undermines the definitions of a circle. The third option incorrectly states that the diameter is half the radius, which contradicts the established relationship. Lastly, the fourth option incorrectly implies that the diameter and radius do not have a defined relationship, which is fundamental in circle geometry. Thus, the correct understanding is that the diameter is explicitly twice the radius.