1. **Problem:** What is the relationship between the radius and diameter of a circle? 2. **Formula and Explanation:** The diameter $d$ of a circle is twice the radius $r$. This is because the diameter spans the entire circle through its center, while the radius extends from the center to the edge. $$d = 2r$$ 3. **Intermediate Work:** If you know the radius, multiply by 2 to get the diameter. 4. **Plain Explanation:** Imagine the radius as a line from the center to the edge of the circle. The diameter is just two of these radii put together, stretching across the circle. 5. **Final Answer:** The diameter is twice the radius, or $d = 2r$.