Respuesta :
Answer:
24π inches
Step-by-step 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 = [tex]\pi r^{2}[/tex]
[tex]144\pi = \pi r^{2}[/tex]
[tex]r^{2}[/tex] = 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!
Correct Question :
The area of a circle is 144π in². What is the circumference, in inches? Express your answer in terms of pi.
[tex] \: [/tex]
Step-by-step explanation:
Before finding the circumference of the circle, we have to find the radius of it.
We already know that,
[tex] \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \pi r{}^{2} = \: \: Area_{(circle)}}}}}} \: \: \bigstar \\ \\ [/tex]
So, using this formula we'll find the radius and now we'll substitute the given values :
[tex] \longrightarrow \qquad{ \sf{ \pi \times r{}^{2} = \: 144 \pi }} \\ \\[/tex]
Cancelling π from both sides we get :
[tex]\longrightarrow \qquad{ \sf{ \cancel\pi \times r{}^{2} = \: 144 \cancel\pi }} \\ \\[/tex]
[tex]\longrightarrow \qquad{ \sf{ r{}^{2} = \: 144 }} \\ \\ [/tex]
[tex]\longrightarrow \qquad{ \sf{ r{}^{} = \: \sqrt{144} }} \\ \\ [/tex]
[tex]\longrightarrow \qquad{ \sf{ \pmb{ r{}^{} = \: 12 }}} \\ \\ [/tex]
So,
- The radius of the circle is 12 inches.
[tex] \\ [/tex]
Now we'll find the circumference of the circle :
[tex] \\{ \longrightarrow \qquad{ \underline {\boxed{ \pmb{ \mathfrak{ \: \: Circumference_{(circle)} = 2 \pi r}}}}}} \: \: \bigstar \\ \\ [/tex]
Now, we'll substitute the required values in the formula :
[tex] \\ { \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 2 \times \pi \times 12}}} \: \: \\ \\ [/tex]
[tex]{ \longrightarrow \qquad{ \sf{ \: \: Circumference_{(circle)} = 2 \times 12 \pi }}} \: \: \\ \\ [/tex]
[tex]{ \longrightarrow \qquad{ \sf{ \pmb{ \: \: Circumference_{(circle)} = 24 \pi }}}} \: \: \\ \\ [/tex]
Therefore,
- The circumference of the circle is 24π inches
