Question

Marcus and three of his friends are guessing the radius of a circular pond. They read that the circumference is 157 ft, so they can use the equation 3.14⋅2r=1573.14⋅2r=157  to determine which of their guesses, which form the replacement set {20, 25, 30, 35}{20, 25, 30, 35}, is correct.

What is the radius of the pond?

The equation given for the circumference of the circular pond is:

\[
2 \cdot 3.14 \cdot r = 157
\]

Where:
- \( r \) is the radius,
- \( 2 \cdot 3.14 \) represents the value of \( 2\pi \), and
- 157 ft is the circumference.

### Step 1: Solve for the radius \( r \)

We can solve for \( r \) by dividing both sides of the equation by \( 2 \cdot 3.14 \):

\[
r = \frac{157}{2 \cdot 3.14}
\]
\[
r = \frac{157}{6.28}
\]
\[
r \approx 25
\]

### Step 2: Conclusion

The radius of the pond is approximately 25 feet, which matches one of the guesses from the replacement set \( \{20, 25, 30, 35\} \).

Therefore, **the correct guess is 25 feet**.

Would you like more details or have any questions? Here are 5 related questions to think about:

1. What would the circumference be if the radius were 30 feet?
2. How would the equation change if the circumference was doubled?
3. How can we calculate the area of the pond if we know the radius is 25 feet?
4. What if the pond were a semicircle—how would that affect the equation for circumference?
5. How does the value of \( \pi \) affect the accuracy of the radius calculation?

**Tip:** Always double-check that you correctly substitute values when solving equations for better accuracy.

Marcus and three of his friends are guessing the radius of a circular pond. They read that the circumference is 157 ft, so they can use the equation 3.14⋅2r=157 to determine which of their guesses, which form the replacement set {20, 25, 30, 35}, is correct. What is the radius of the pond?

Discover how to calculate the radius of a circular pond given the circumference of 157 feet. Using the formula C = 2πr, this problem covers important geometry concepts and algebraic manipulation. Suitable for students in Grades 6-8.

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