Question

The area of a circle is 144 in 2. What is the circumference, in inches? Express you answer in terms of pi.

Answer 1

Correct Question :

The area of a circle is 144π in². What is the circumference, in inches? Express your answer in terms of pi.

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Explanation:

Before finding the circumference of the circle, we have to find the radius of it.

We already know that,

`\longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \pi r{}^(2) = \: \: Area_((circle))}}}}} \: \: \bigstar \\ \\`

So, using this formula we'll find the radius and now we'll substitute the given values :

`\longrightarrow \qquad{ \sf{ \pi * r{}^(2) = \: 144 \pi }} \\ \\`

Cancelling π from both sides we get :

`\longrightarrow \qquad{ \sf{ \cancel\pi * r{}^(2) = \: 144 \cancel\pi }} \\ \\`

`\longrightarrow \qquad{ \sf{ r{}^(2) = \: 144 }} \\ \\`

`\longrightarrow \qquad{ \sf{ r{}^{} = \: √(144) }} \\ \\`

`\longrightarrow \qquad{ \sf{ \pmb{ r{}^{} = \: 12 }}} \\ \\`

So,

• The radius of the circle is 12 inches.

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Now we'll find the circumference of the circle :

`\\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Circumference_((circle)) = 2 \pi r}}}}}} \: \: \bigstar \\ \\`

Now, we'll substitute the required values in the formula :

`\\ { \longrightarrow \qquad{ \sf{ \: \: Circumference_((circle)) = 2 * \pi * 12}}} \: \: \\ \\`

`{ \longrightarrow \qquad{ \sf{ \: \: Circumference_((circle)) = 2 * 12 \pi }}} \: \: \\ \\`

`{ \longrightarrow \qquad{ \sf{ \pmb{ \: \: Circumference_((circle)) = 24 \pi }}}} \: \: \\ \\`

Therefore,

• The circumference of the circle is 24π inches

Answer 2

24π inches

Explanation:

The area of a circle is denoted by: , where r is the radius. Here, we know that the area is A = , so we can plug this in to find r:

A =
`\pi r^(2)`

`144\pi = \pi r^(2)`

`r^(2)` = 144

r = 12

The circumference is denoted by: , where r is the radius. We've found the radius so just plug 12 in for r:

Thus, the circumference is 24π inches.

Hope this helps!