• $A = \frac{r^{2} \cdot \pi \cdot \alpha }{ 360}$
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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: 06
$\text{Gegeben:}\\\text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Radius} \qquad r \qquad [m] \\ \\ \text{Gesucht:} \\\text{Fläche} \qquad A \qquad [m^{2}] \\ \\ A = \frac{r^{2} \cdot \pi \cdot \alpha }{ 360}\\ \textbf{Gegeben:} \\ \alpha=30^{\circ} \qquad \pi=3\frac{16}{113} \qquad r=32m \qquad \\ \\ \textbf{Rechnung:} \\ A = \frac{r^{2} \cdot \pi \cdot \alpha }{ 360} \\ \alpha=30^{\circ}\\ \pi=3\frac{16}{113}\\ r=32m\\ A = \frac{(32m)^{2} \cdot 3\frac{16}{113} \cdot 30^{\circ} }{ 360}\\\\A=268m^{2} \\\\\\ \small \begin{array}{|l|} \hline alpha=\\ \hline 30 ° \\ \hline 1,8\cdot 10^{3} \text{'} \\ \hline 1,08\cdot 10^{5} \text{''} \\ \hline 33\frac{1}{3} gon \\ \hline 0,524 rad \\ \hline \end{array} \small \begin{array}{|l|} \hline r=\\ \hline 32 m \\ \hline 320 dm \\ \hline 3,2\cdot 10^{3} cm \\ \hline 3,2\cdot 10^{4} mm \\ \hline 3,2\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 268 m^2 \\ \hline 2,68\cdot 10^{4} dm^2 \\ \hline 2,68\cdot 10^{6} cm^2 \\ \hline 268082577\frac{1}{15} mm^2 \\ \hline 2,68 a \\ \hline 0,0268 ha \\ \hline \end{array}$