Let's solve the problem step by step:
1. Identify the Diameter and Calculate the Radius:
The diameter of the circle is given as [tex]\(4 \, \text{ft}\)[/tex]. The radius is half of the diameter. Therefore:
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{4}{2} = 2 \, \text{ft}
\][/tex]
2. Use the Formula for the Area of a Circle:
The formula to calculate the area [tex]\(A\)[/tex] of a circle is given by:
[tex]\[
A = \pi r^2
\][/tex]
where [tex]\(r\)[/tex] is the radius of the circle.
3. Substitute the Radius into the Formula:
We have a radius [tex]\( r = 2 \, \text{ft} \)[/tex]. Substituting this value into the formula gives:
[tex]\[
A = \pi (2)^2
\][/tex]
[tex]\[
A = \pi \cdot 4
\][/tex]
4. Approximate the Area:
We know from given information that [tex]\(\pi \cdot 4 \approx 12.566370614359172 \)[/tex]. Therefore, the area is approximately:
[tex]\[
A \approx 12.6 \, \text{ft}^2
\][/tex]
So, the amount of ground that the circular fire pit will cover is closest to:
[tex]\[
12.6 \, \text{ft}^2
\][/tex]
Thus, the correct answer is:
[tex]\[
12.6 \, \text{ft}^2
\][/tex]
