+9479 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
+26387 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
\(\begin{array}{|rcll|} \hline C &=& 2\pi r \quad &| \quad r=\sqrt{\frac{A}{\pi}} \\ C &=& 2\pi\sqrt{\frac{A}{\pi}} \\ C &=& 2\sqrt{\pi^2\frac{A}{\pi}} \\ \mathbf{C }& \mathbf{=} & \mathbf{2\sqrt{A\cdot \pi }} \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline \mathbf{C }& \mathbf{=} & \mathbf{2\sqrt{A\cdot \pi }} \quad & | \quad A = 25.12 \\ C &=& 2\sqrt{25.12\cdot 3.14159265359} \\ C &=& 2\sqrt{78.9168074582} \\ C &=& 2\cdot 8.88351323848 \\ C &=& 17.7670264770 \\ \hline \end{array}\)
