The circumference of a circular field is 175.84 yards. What is the radius of the field? Use 3.14 for  pi and do not round your answer.

The formula for the circumference \( C \) of a circle is given by:

\[
C = 2\pi r
\]

Where:
- \( C \) is the circumference,
- \( r \) is the radius,
- \( \pi \) is approximately 3.14.

You are given that the circumference \( C = 175.84 \) yards. Substituting the values into the formula:

\[
175.84 = 2 \times 3.14 \times r
\]

Now, solve for \( r \):

\[
r = \frac{175.84}{2 \times 3.14}
\]

First calculate the denominator:

\[
2 \times 3.14 = 6.28
\]

Now divide:

\[
r = \frac{175.84}{6.28} = 28
\]

So, the radius of the field is \( 28 \) yards.

Would you like more details, or do you have any questions?

Here are five related questions to explore:
1. What would the radius be if the circumference were 300 yards?
2. How do you calculate the area of a circle given its radius?
3. How would the radius change if the circumference doubled?
4. What is the relationship between diameter and circumference?
5. Can the formula for circumference be used to calculate the radius of any shape other than a circle?

**Tip:** Always remember to check units in geometry problems to ensure consistency throughout the calculations.

The circumference of a circular field is 175.84 yards. What is the radius of the field? Use 3.14 for pi and do not round your answer.

Learn how to calculate the radius of a circular field with a circumference of 175.84 yards using the formula C = 2πr. This step-by-step solution explains the process, using 3.14 for pi. Ideal for students in Grades 6-8 exploring geometry concepts.

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