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The problem asks to write a formula expressing that the diameter \( d \) of a circle is directly proportional to the circumference \( C \), using \( k \) to denote the constant of proportionality.

By definition, when two quantities are directly proportional, their ratio is constant. This relationship can be written as:

\[
d = k \cdot C
\]

where:
- \( d \) is the diameter,
- \( C \) is the circumference,
- \( k \) is the constant of proportionality.

In the case of a circle, we know from geometry that the relationship between the diameter and the circumference is given by:

\[
C = \pi \cdot d
\]

Thus, \( k = \frac{1}{\pi} \), which gives us the specific value of the constant \( k \) in the general formula.

Would you like further details or have any questions about this?

Here are 5 related questions you might find helpful:
1. How is the circumference of a circle derived from the diameter?
2. What is the constant of proportionality in direct proportionality problems?
3. Can you derive the formula for the circumference in terms of the radius?
4. What are some real-world applications of direct proportionality?
5. How can we solve for the diameter if the circumference is known?

**Tip**: In any direct proportion problem, identifying the constant helps form the relationship between two variables quickly.

The diameter, d, of a circle is directly proportional to the circumference, C. Use k to denote the constant of proportionality.

This page provides a detailed explanation of how to write a formula that expresses the direct proportionality between the diameter and circumference of a circle. Suitable for students in Grades 6-8, the explanation covers key concepts such as direct proportionality and the geometry of circles.

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