What is the relation between the diameter and circumference of a circle?

Options

A. `C=2pid`
B. `C=pid`
C. `C=(pid)/2`
D. `C=(pid^2)/2`

Answer

To find the relation between the diameter and circumference of a circle, we can follow these steps:

### Step 1: Understand the definitions
- The **circumference (C)** of a circle is the distance around the circle.
- The **diameter (d)** of a circle is the distance across the circle through its center.

### Step 2: Relate diameter to radius
- The radius (r) of a circle is half of the diameter.
\[ r = \frac{d}{2} \]

### Step 3: Use the formula for circumference
- The formula for the circumference of a circle in terms of the radius is:
\[ C = 2\pi r \]

### Step 4: Substitute the radius in the circumference formula
- Substitute \( r = \frac{d}{2} \) into the circumference formula:
\[ C = 2\pi \left(\frac{d}{2}\right) \]

### Step 5: Simplify the equation
- Simplifying the equation gives:
\[ C = \pi d \]

### Conclusion
- Therefore, the relation between the diameter and circumference of a circle is:
\[ C = \pi d \]