The circumference of a circular field is 204.1 yards. What is the radius of the field? Use 3.14 for π and do not round your answer.

1. Break Down the Problem

To find the radius of the circular field, we can use the formula for the circumference of a circle:

$C = 2\pi r$

where $C$ is the circumference and $r$ is the radius.

2. Relevant Concepts

We know the circumference $C = 204.1$ yards and $\pi \approx 3.14$. We need to solve for $r$.

3. Analysis and Detail

Rearranging the formula to solve for $r$:

$r = \frac{C}{2\pi}$

Substituting the known values:

$r = \frac{204.1}{2 \times 3.14}$

Calculating the denominator:

$2 \times 3.14 = 6.28$

Now, substituting this back into the formula:

$r = \frac{204.1}{6.28}$

Performing the division:

$r \approx 32.5$

4. Verify and Summarize

We calculated $r$ as approximately $32.5$ yards. The derived steps confirm that the radius is correct given the circumference.

Final Answer

The radius of the field is $32.5$ yards.