77.4k views
10 votes
The area of a circle is 64π in². What is the circumference, in inches? Express your answer in terms of \piπ.

2 Answers

5 votes

Answer:

8

Explanation:

The area of a circle is
\pi

So we can divide 64
\pi by
\pi and have 64.

Now take the square root of 64 and its 8

User Kibibu
by
7.9k points
5 votes

Answer:

the is 16 pie

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.

User SteveBering
by
8.4k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories