Which of the following equations represents the relationship between the circumference and diameter of a circle?

The relationship between the circumference (C) and the diameter (d) of a circle is indeed represented by the equation C = πd. This formula expresses that the circumference is directly proportional to the diameter, where π (pi) is a mathematical constant approximately equal to 3.14159.

Understanding this relationship is fundamental in geometry; it shows how the linear distance around the circle is determined by its diameter. Knowing the diameter allows you to calculate the circumference by simply multiplying by π. This equation captures the essence of how circles function mathematically.

The other equations provided relate to the circumference but do so in different contexts. For example, C = 2πr gives the circumference in terms of the radius (r) instead of the diameter, while C = πr² defines the area of the circle, which is a different concept altogether. Lastly, C = 2d does not represent the circumference as it suggests a direct measurement of diameter rather than accounting for pi.