Question

If the circumference of a circle is 198 feet then what is the area to the nearest square foot

Answer 1

To find the area of a circle from its circumference, we can follow these steps:

1. First, recall the formula for the circumference of a circle:
\[
C = 2\pi r
\]
Where \( C \) is the circumference and \( r \) is the radius.

2. Rearranging the formula to solve for the radius gives:
\[
r = \frac{C}{2\pi}
\]

3. Substitute the given circumference (198 feet) into the formula:
\[
r = \frac{198}{2\pi} = \frac{198}{2 \times 3.14159} \approx \frac{198}{6.28318} \approx 31.57 \text{ feet}
\]

4. Now, calculate the area \( A \) of the circle using the area formula:
\[
A = \pi r^2
\]

5. Substitute the radius we calculated:
\[
A \approx \pi (31.57)^2 \approx 3.14159 \times 997.4649 \approx 3139.59 \text{ square feet}
\]

6. Rounding the area to the nearest square foot:
\[
A \approx 3140 \text{ square feet}
\]

Thus, the area of the circle is approximately **3140 square feet**.