Question

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

32 ft.2
32 ft. squared

63 ft.2
63 ft. squared

3,120 ft.2
3,120 ft. squared

99 ft.2

Answer 1

To find the area of the circle given its circumference, we can use the following formulas:

1. **Circumference formula**: \( C = 2\pi r \)
2. **Area formula**: \( A = \pi r^2 \)

Given that the circumference \( C \) is 198 feet, we first find the radius \( r \).

Using the circumference formula:

\[
198 = 2\pi r
\]

Now, we can solve for \( r \):

\[
r = \frac{198}{2\pi} = \frac{99}{\pi}
\]

Next, we can find the area \( A \) using the radius:

\[
A = \pi r^2 = \pi \left(\frac{99}{\pi}\right)^2 = \pi \cdot \frac{9801}{\pi^2} = \frac{9801}{\pi}
\]

Now, we can calculate the area more easily by using \( \pi \approx 3.14 \):

\[
A \approx \frac{9801}{3.14} \approx 3120.06
\]

Rounding to the nearest square foot gives:

\[
A \approx 3120 \, \text{ft}^2
\]

Therefore, the area of the circle is approximately **3,120 ft²**.

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