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 3,120 ft.2 3,120 ft. squared 32 ft.2 32 ft. squared 99 ft.2

Answer 1

To find the area of the circle, we start with the given circumference \( C \) of the circle:

\[
C = 198 \text{ feet}
\]

The formula for the circumference of a circle is:

\[
C = 2\pi r
\]

Where \( r \) is the radius of the circle. We can solve for \( r \):

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

Next, we will use the radius to find the area \( A \) of the circle. The formula for the area of a circle is:

\[
A = \pi r^2
\]

Substituting our expression for \( r \):

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

Now, we will compute the area using \( \pi \approx 3.14 \):

\[
A \approx \frac{9801}{3.14} \approx 3111.69
\]

Rounding this to the nearest square foot:

\[
A \approx 3112 \text{ ft}^2
\]

However, none of the options directly provided include this value. We can use a more precise value for \( \pi \approx 3.14159 \):

\[
A \approx \frac{9801}{3.14159} \approx 3111.00
\]

So rounding to the nearest square foot still gives about **3111 ft²**.

Given the closest area to the options provided in your question, the correct answer is:

**3,120 ft²**.