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# Circle circumference

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

Guest Mar 15, 2017
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#1
+4155
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circumference = 2π√(25.12/π)

circumference ≈ 17.767

hectictar  Mar 15, 2017
#2
+18369
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

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

2. Circumference

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

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

heureka  Mar 15, 2017

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