• $A = \frac{r^{2} \cdot \pi \cdot \alpha }{ 360}$
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$r = \sqrt{\frac{A\cdot 360}{\alpha \cdot \pi }}$
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$\alpha = \frac{A\cdot 360}{r^{2} \cdot \pi }$
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$b = \frac{2\cdot r\cdot \pi \cdot \alpha }{ 360}$
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$r = \frac{b\cdot 360}{\alpha \cdot \pi \cdot 2}$
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$\alpha = \frac{b\cdot 360}{r\cdot \pi \cdot 2}$
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Beispiel Nr: 03
$\text{Gegeben:}\\\text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Radius} \qquad r \qquad [m] \\ \text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ \text{Gesucht:} \\\text{Kreisbogen} \qquad b \qquad [m] \\ \\ b = \frac{2\cdot r\cdot \pi \cdot \alpha }{ 360}\\ \textbf{Gegeben:} \\ \pi=3\frac{16}{113} \qquad r=12m \qquad \alpha=90^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\ b = \frac{2\cdot r\cdot \pi \cdot \alpha }{ 360} \\ \pi=3\frac{16}{113}\\ r=12m\\ \alpha=90^{\circ}\\ b = \frac{2\cdot 12m\cdot 3\frac{16}{113} \cdot 90^{\circ} }{ 360}\\\\b=18,8m \\\\ \small \begin{array}{|l|} \hline r=\\ \hline 12 m \\ \hline 120 dm \\ \hline 1,2\cdot 10^{3} cm \\ \hline 1,2\cdot 10^{4} mm \\ \hline 1,2\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 90 ° \\ \hline 5,4\cdot 10^{3} \text{'} \\ \hline 3,24\cdot 10^{5} \text{''} \\ \hline 100 gon \\ \hline 1,57 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 18,8 m \\ \hline 188 dm \\ \hline 1,88\cdot 10^{3} cm \\ \hline 1,88\cdot 10^{4} mm \\ \hline 18849556\frac{1}{5} \mu m \\ \hline \end{array}$