To find the area of a circle given its circumference, we can use the following formulas:
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Circumference \(C\) of a circle is given by: \[ C = 2\pi r \] where \(r\) is the radius.
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Area \(A\) of a circle is given by: \[ A = \pi r^2 \]
First, we can find the radius \(r\) using the circumference: \[ 198 = 2\pi r \] Solving for \(r\): \[ r = \frac{198}{2\pi} = \frac{99}{\pi} \]
Next, we can calculate the area 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 need to calculate this value numerically. Using \(\pi \approx 3.14\): \[ A \approx \frac{9801}{3.14} \approx 3121.66 \]
Rounding this to the nearest square foot gives us: \[ A \approx 3122 \text{ ft.}^2 \]
Thus, the closest response would be: 3,120 ft.² (as it's the closest whole number option available among the choices).