Question

The area of a circle is 1217 ft2. What is the circumference, in feet? Express your answer in terms of .

Answer 1

`\text{Circumference}=\sqrt[]{4868\pi^{}}\text{ f}eet`

Step-by-step explanation

Step 1

the area of a circle is given by

`\begin{gathered} \text{Area}_(circle)=\pi r^2=\pi((d^2)/(4)) \\ \text{where r is the radius and d is the diameter} \end{gathered}`

and the circumference is given by

`\text{Circumference}=\text{ }\pi\cdot diameter`

then

let

Area=1217 square feet

replace, and isolate diameter

`\begin{gathered} \text{Area}_(circle)\pi((d^2)/(4)) \\ \text{1217=}\pi((d^2)/(4)) \\ Mu\text{ltiply both sides by 4} \\ \text{1217}\cdot4\text{=}\pi((d^2)/(4))\cdot4 \\ 4868=\pi d^2 \\ \text{divide both sides by }\pi \\ (4868)/(\pi)=(\pi d^2)/(\pi) \\ (4868)/(\pi)=d^2 \\ \text{square root in both sides} \\ \sqrt{(4868)/(\pi)}=√(d^2) \\ \sqrt[]{(4868)/(\pi)}=\text{diameter} \\ \end{gathered}`

Step 2

now, we have the diameter, replace it in the circumference formula

let

diameter=39.36 ft

replace

`\begin{gathered} \text{Circumference}=\text{ }\pi\cdot diameter \\ \text{Circumference}=\text{ }\pi\cdot\sqrt[]{(4868)/(\pi)} \\ \text{Circumference}=\sqrt[]{(4868\pi^2)/(\pi)} \\ \text{Circumference}=\sqrt[]{4868\pi^{}} \end{gathered}`

I hope this helps you