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The area of a circle is 64π in². What is the circumference, in inches? Express your answer in terms of \piπ.

Sagot :

Answer:

8

Step-by-step explanation:

The area of a circle is [tex]\pi[/tex]r²

So we can divide 64[tex]\pi[/tex] by [tex]\pi[/tex] and have 64.

Now take the square root of 64 and its 8

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.