The circumference of a circular yard is approximately 24 feet. What is the approximate area inside the circular yard?

To find the approximate area inside the circular yard, we can use the relationship between the circumference and the area of a circle.

Given:
- The circumference \( C = 24 \) feet.

The formula for the circumference of a circle is:

\[
C = 2\pi r
\]

Where:
- \( C \) is the circumference,
- \( r \) is the radius of the circle, and
- \( \pi \approx 3.14159 \).

We can solve for the radius \( r \) using the formula:

\[
r = \frac{C}{2\pi}
\]

Substitute the given circumference:

\[
r = \frac{24}{2\pi} \approx \frac{24}{6.28318} \approx 3.82 \text{ feet}
\]

Now that we have the radius, we can find the area of the circle using the formula:

\[
A = \pi r^2
\]

Substitute the radius \( r = 3.82 \) feet:

\[
A \approx \pi (3.82)^2 \approx 3.14159 \times 14.59 \approx 45.85 \text{ square feet}
\]

Thus, the approximate area inside the circular yard is **45.85 square feet**.

Would you like further details or have any questions?

Here are 5 related questions:
1. How does the area change if the circumference is doubled?
2. What is the formula for the area of a circle in terms of circumference?
3. How would the area calculation differ if the yard were elliptical?
4. What is the approximate diameter of the yard based on the given circumference?
5. How accurate is the approximation using \( \pi \approx 3.14 \) compared to using the exact value of \( \pi \)?

**Tip**: To quickly estimate the area from the circumference, use the formula \( A = \frac{C^2}{4\pi} \).

The circumference of a circular yard is approximately 24 feet. What is the approximate area inside the circular yard?

Find out how to calculate the approximate area of a circular yard with a 24-foot circumference using key geometric formulas. This solution walks through the steps to derive the radius and compute the area, suitable for students in Grades 6-8.

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