Question

If the circumference of a circle is 198 feet, then what is the area to the nearest square foot?(1 point) Responses 99 ft.2 99 ft. squared 3,120 ft.2 3,120 ft. squared 32 ft.2 32 ft. squared 63 ft.2

Answer 1

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

1. The formula for the circumference \( C \) of a circle is:
\[
C = 2\pi r
\]
where \( r \) is the radius.

2. To find the radius, rearranging the formula gives:
\[
r = \frac{C}{2\pi}
\]

3. Plugging in the circumference:
\[
r = \frac{198}{2\pi} = \frac{198}{2 \cdot 3.14} \approx \frac{198}{6.28} \approx 31.55 \text{ feet}
\]

4. Next, we use the formula for the area \( A \) of a circle:
\[
A = \pi r^2
\]

5. Calculating the area using the radius we found:
\[
A = \pi (31.55)^2 \approx 3.14 \times 996.60 \approx 3,128.86 \text{ square feet}
\]

Rounding to the nearest square foot:
\[
A \approx 3,129 \text{ square feet}
\]

Among the choices provided, the closest value is **3,120 ft. squared**.