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 63 ft.2 63 ft. squared 32 ft.2

Answer 1

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

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

2. The formula for the area (A) of a circle is:
\[
A = \pi r^2
\]

Given that the circumference \( C \) is 198 feet, we can first solve for the radius \( r \):

\[
198 = 2\pi r
\]

Now we can solve for \( r \):

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

Next, we will use this radius to find the area \( A \):

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

Now, we need to calculate this value:

Using \( \pi \approx 3.14 \):

\[
A \approx \frac{9801}{3.14} \approx 3121.65
\]

Rounding to the nearest square foot, we get \( A \approx 3122 \) square feet.

Hence, the closest answer from the responses would be:
**3,120 ft. squared**.