Answer:
the is 16 pie
Step-by-step explanation:
To find the circumference, we would use the formula:
\color{green}{C}=
C=
\,\,2\pi\color{red}{r}
2πr
Circumference of a Circle formula
But we don't know the radius yet. We do know the area, so we can use the area formula to find the radius:
\color{purple}{A}=
A=
\,\,\pi \color{red}{r}^{2}
πr
2
Area of a Circle formula
\color{purple}{64\pi}=
64π=
\,\,\pi \cdot \color{red}{r}^{2}
π⋅r
2
Substitute given circumference into formula
\frac{\color{purple}{64\cdot \pi}}{ \pi}=
π
64⋅π
=
\,\,\frac{\pi \cdot \color{red}{r}^{2}}{\pi}
π
π⋅r
2
Since \piπ is on both sides, divide both sides by \piπ
64=
64=
\,\,\color{red}{r}^{2}
r
2
Cancel out the \piπs from the top and bottom of each fraction.
\color{red}{r}=
r=
\,\,8
8
Squared means something times itself. What times itself equals 64?
\text{The \color{red}{radius} of the circle is \color{red}{8} feet.}
The radius of the circle is 8 feet.
\text{Now use the radius to find the circumference:}
Now use the radius to find the circumference:
\color{green}{C}=
C=
\,\,2\pi\color{red}{r}
2πr
Circumference of a Circle formula
\color{green}{C}=
C=
\,\,2 \cdot \pi \cdot\color{red}{8}
2⋅π⋅8
Substitute radius into formula
\color{green}{C}=
C=
\,\,2 \cdot\color{red}{8}\cdot \pi
2⋅8⋅π
Commutative property of multiplication
\color{green}{C}=
C=
\,\,16\pi
16π
Final answer in terms of \piπ
\text{The \color{green}{circumference} of the circle is 16\(\pi\) ft.}
The circumference of the circle is 16π ft.
