What is the ratio of a circle's Radius to its circumference?

Options

A. `2pi :1`
B. `1:2pi`
C. `pi :1`
D. `1:pi`

Answer

To find the ratio of a circle's radius to its circumference, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the radius of the circle**: Let the radius of the circle be denoted as \( r \).

2. **Calculate the circumference of the circle**: The formula for the circumference \( C \) of a circle is given by:
\[ C = 2\pi r \]

3. **Set up the ratio**: We need to find the ratio of the radius \( r \) to the circumference \( C \). This can be expressed as:
\[ \text{Ratio} = \frac{r}{C} \]

4. **Substitute the circumference into the ratio**: Replace \( C \) with \( 2\pi r \):
\[ \text{Ratio} = \frac{r}{2\pi r} \]

5. **Simplify the ratio**: The \( r \) in the numerator and denominator cancels out (assuming \( r \neq 0 \)):
\[ \text{Ratio} = \frac{1}{2\pi} \]

6. **Final answer**: Therefore, the ratio of a circle's radius to its circumference is:
\[ \frac{1}{2\pi} \]