Explanation
Step 1
the area of a circle is given by
[tex]\begin{gathered} \text{Area}_{circle}=\pi r^2=\pi(\frac{d^2}{4}) \\ \text{where r is the radius and d is the diameter} \end{gathered}[/tex]and the circumference is given by
[tex]\text{Circumference}=\text{ }\pi\cdot diameter[/tex]then
let
Area=1217 square feet
replace, and isolate diameter
[tex]\begin{gathered} \text{Area}_{circle}\pi(\frac{d^2}{4}) \\ \text{1217=}\pi(\frac{d^2}{4}) \\ Mu\text{ltiply both sides by 4} \\ \text{1217}\cdot4\text{=}\pi(\frac{d^2}{4})\cdot4 \\ 4868=\pi d^2 \\ \text{divide both sides by }\pi \\ \frac{4868}{\pi}=\frac{\pi d^2}{\pi} \\ \frac{4868}{\pi}=d^2 \\ \text{square root in both sides} \\ \sqrt{\frac{4868}{\pi}}=\sqrt{d^2} \\ \sqrt[]{\frac{4868}{\pi}}=\text{diameter} \\ \end{gathered}[/tex]Step 2
now, we have the diameter, replace it in the circumference formula
let
diameter=39.36 ft
replace
[tex]\begin{gathered} \text{Circumference}=\text{ }\pi\cdot diameter \\ \text{Circumference}=\text{ }\pi\cdot\sqrt[]{\frac{4868}{\pi}} \\ \text{Circumference}=\sqrt[]{\frac{4868\pi^2}{\pi}} \\ \text{Circumference}=\sqrt[]{4868\pi^{}} \end{gathered}[/tex]I hope this helps you
