The relation between radius (r) and diameter (d) is___

Options

A. d=2xr
B. d=r/2
C. d=r/3
D. d=3r

Answer

To find the relation between the radius (r) and diameter (d) of a circle, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definitions**:
- The **diameter (d)** of a circle is defined as the longest distance across the circle, passing through the center. It connects two points on the circle.
- The **radius (r)** of a circle is defined as the distance from the center of the circle to any point on its circumference.

2. **Visualize the Circle**:
- Imagine a circle with a center point. Draw a line from the center to the edge of the circle. This line represents the radius (r).
- Now, draw a line that passes through the center and touches both ends of the circle. This line represents the diameter (d).

3. **Relate Radius to Diameter**:
- If you consider the diameter, it is made up of two radii. That is, if you start from one edge of the circle, go to the center (which is one radius), and then from the center to the other edge (which is another radius).
- Therefore, the diameter can be expressed as the sum of two radii:
\[ d = r + r \]

4. **Simplify the Equation**:
- Since \( r + r \) is the same as \( 2r \), we can rewrite the equation as:
\[ d = 2r \]

5. **Conclusion**:
- The relation between the radius and diameter of a circle is:
\[ d = 2r \]