Question

If the circumference of a circle is 198 feet, then what is the area to the nearest square foot?

a.32 ft.^2
b. 3,120 ft.^2
c. 63 ft.^2
d. 99 ft.^2

Answer 1

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

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

First, we need to find the radius (r) of the circle using the given circumference:

\[
C = 198 \text{ feet}
\]
\[
2\pi r = 198
\]

Now, solving for \(r\):

\[
r = \frac{198}{2\pi} = \frac{198}{2 \times 3.14159} \approx \frac{198}{6.28318} \approx 31.6 \text{ feet}
\]

Next, we calculate the area using the radius:

\[
A = \pi r^2
\]
\[
A = \pi (31.6)^2 \approx 3.14159 \times 998.56 \approx 3136.26 \text{ square feet}
\]

Now, rounding to the nearest square foot, we get:

\[
A \approx 3136 \text{ ft}^2
\]

However, it seems that the options provided are significantly lower than this result. Let's double check one more calculation:

1. We have computed the radius based on a given circumference of 198 feet.
2. Verification of area:
- Using precise value of r = 31.6 ft?
- \( (31.6)^2 \approx 998.56\)
- Area \( \approx 3.14159 \cdot 998.56 \approx 3136.26 \) correct and final.

Since \( 3120 \text{ ft}^2 \) is the closest to our calculation from among the options, the answer is:

**b. 3,120 ft²**