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If 25.12 is the area of a circle, what is the circumference?

Guest Mar 15, 2017
 #1
avatar+7155 
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area = π(radius)2

25.12 = π(radius)2

25.12/π = radius2

√(25.12/π) = radius

 

circumference = 2π(radius)

circumference = 2π√(25.12/π)

circumference ≈ 17.767

hectictar  Mar 15, 2017
 #2
avatar+19645 
0

If 25.12 is the area of a circle, what is the circumference?

 

Let A = 25.12 the area of a circle

Let C = circumference of a circle

 

1. Radius r = ?

\(\begin{array}{|rcll|} \hline A &=& \pi r^2 \\ \frac{A}{\pi} &=& r^2 \\ \mathbf{\sqrt{\frac{A}{\pi} } } & \mathbf{=} & \mathbf{r} \\ \hline \end{array}\)

 

2. Circumference

\(\begin{array}{|rcll|} \hline C &=& 2\pi r \quad &| \quad r=\sqrt{\frac{A}{\pi}} \\ C &=& 2\pi\sqrt{\frac{A}{\pi}} \\ C &=& 2\sqrt{\pi^2\frac{A}{\pi}} \\ \mathbf{C }& \mathbf{=} & \mathbf{2\sqrt{A\cdot \pi }} \\ \hline \end{array}\)

 

\(\begin{array}{|rcll|} \hline \mathbf{C }& \mathbf{=} & \mathbf{2\sqrt{A\cdot \pi }} \quad & | \quad A = 25.12 \\ C &=& 2\sqrt{25.12\cdot 3.14159265359} \\ C &=& 2\sqrt{78.9168074582} \\ C &=& 2\cdot 8.88351323848 \\ C &=& 17.7670264770 \\ \hline \end{array}\)

 

laugh

heureka  Mar 15, 2017

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