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
3,120 ft. squared

Answer 1

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

1. **Circumference of the circle** is given by:
\[
C = 2\pi r
\]
where \( r \) is the radius.

2. We know the circumference \( C = 198 \) feet:
\[
198 = 2\pi r
\]
Solving for \( r \):
\[
r = \frac{198}{2\pi} = \frac{99}{\pi}
\]

3. **Area of the circle** is given by:
\[
A = \pi r^2
\]
Substituting \( r \):
\[
A = \pi \left(\frac{99}{\pi}\right)^2 = \pi \cdot \frac{9801}{\pi^2} = \frac{9801}{\pi}
\]

4. Using \( \pi \approx 3.14 \):
\[
A \approx \frac{9801}{3.14} \approx 3120.06
\]

Therefore, the area of the circle to the nearest square foot is approximately **3,120 ft²**.

So, the correct response is:
**3,120 ft.²**