Question

If the circumference of a circle is 198 feet, then what is the area to the nearest square foot?(1 point)
Responses

63 ft.2
63 ft. squared

99 ft.2
99 ft. squared

32 ft.2
32 ft. squared

3,120 ft.2

Answer 1

To find the area of a circle when the circumference is given, we can use the formulas for circumference and area of a circle.

The formulas are as follows:
- Circumference \( C = 2\pi r \)
- Area \( A = \pi r^2 \)

1. **Find the radius using the circumference**:
\[
C = 2\pi r
\]
Given that \( C = 198 \) feet,
\[
198 = 2\pi r
\]
To find \( r \), we rearrange the formula:
\[
r = \frac{198}{2\pi} = \frac{99}{\pi}
\]

2. **Calculate the area**:
\[
A = \pi r^2
\]
Substituting \( r \):
\[
A = \pi \left(\frac{99}{\pi}\right)^2 = \pi \frac{9801}{\pi^2} = \frac{9801}{\pi}
\]
Now, substitute \( \pi \approx 3.14 \):
\[
A \approx \frac{9801}{3.14} \approx 3120.06
\]
Rounding to the nearest square foot gives \( A \approx 3120 \) ft².

Thus, the correct response is **3,120 ft.²**.