To determine the diameter of the circle given that its area is 201.0624 square feet and using [tex]\(\pi = 3.1416\)[/tex], follow these steps:
1. Recall the formula for the area of a circle:
[tex]\[
A = \pi r^2
\][/tex]
where [tex]\(A\)[/tex] is the area and [tex]\(r\)[/tex] is the radius of the circle.
2. Rearrange the formula to solve for the radius [tex]\(r\)[/tex]:
[tex]\[
r = \sqrt{\frac{A}{\pi}}
\][/tex]
3. Substitute the given values:
[tex]\[
r = \sqrt{\frac{201.0624}{3.1416}}
\][/tex]
4. Calculate the radius:
[tex]\[
r = \sqrt{64} = 8 \, \text{feet}
\][/tex]
5. Now, recall the relationship between diameter and radius:
[tex]\[
d = 2r
\][/tex]
where [tex]\(d\)[/tex] is the diameter.
6. Using the calculated radius, find the diameter:
[tex]\[
d = 2 \times 8 = 16 \, \text{feet}
\][/tex]
Thus, the diameter of the circle is [tex]\(16\)[/tex] feet. The correct answer is:
B) 16 feet
