• $A = \frac{r^{2} \cdot \pi \cdot \alpha }{ 360}$
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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: 02
$\text{Gegeben:}\\\text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Radius} \qquad r \qquad [m] \\ \text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ \text{Gesucht:} \\\text{Kreisbogen} \qquad b \qquad [m] \\ \\ b = \frac{2\cdot r\cdot \pi \cdot \alpha }{ 360}\\ \textbf{Gegeben:} \\ \pi=3\frac{16}{113} \qquad r=2\frac{1}{2}m \qquad \alpha=30^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\ b = \frac{2\cdot r\cdot \pi \cdot \alpha }{ 360} \\ \pi=3\frac{16}{113}\\ r=2\frac{1}{2}m\\ \alpha=30^{\circ}\\ b = \frac{2\cdot 2\frac{1}{2}m\cdot 3\frac{16}{113} \cdot 30^{\circ} }{ 360}\\\\b=1,31m \\\\ \small \begin{array}{|l|} \hline r=\\ \hline 2\frac{1}{2} m \\ \hline 25 dm \\ \hline 250 cm \\ \hline 2,5\cdot 10^{3} mm \\ \hline 2,5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline alpha=\\ \hline 30 ° \\ \hline 1,8\cdot 10^{3} \text{'} \\ \hline 1,08\cdot 10^{5} \text{''} \\ \hline 33\frac{1}{3} gon \\ \hline 0,524 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 1,31 m \\ \hline 13,1 dm \\ \hline 131 cm \\ \hline 1,31\cdot 10^{3} mm \\ \hline 1308996\frac{23}{24} \mu m \\ \hline \end{array}$