Geometrie-Kreis-Kreissektor (Grad)


  • $A = \frac{r^{2} \cdot \pi \cdot \alpha }{ 360}$
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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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    $\alpha = \frac{b\cdot 360}{r\cdot \pi \cdot 2}$
    1 2 3 4

Beispiel Nr: 04
$ \text{Gegeben:}\\\text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Kreisbogen} \qquad b \qquad [m] \\ \text{Winkel} \qquad \alpha \qquad [^{\circ}] \\ \\ \text{Gesucht:} \\\text{Radius} \qquad r \qquad [m] \\ \\ r = \frac{b\cdot 360}{\alpha \cdot \pi \cdot 2}\\ \textbf{Gegeben:} \\ \pi=3\frac{16}{113} \qquad b=7\frac{1}{2}m \qquad \alpha=90^{\circ} \qquad \\ \\ \textbf{Rechnung:} \\ r = \frac{b\cdot 360}{\alpha \cdot \pi \cdot 2} \\ \pi=3\frac{16}{113}\\ b=7\frac{1}{2}m\\ \alpha=90^{\circ}\\ r = \frac{7\frac{1}{2}m\cdot 360}{90^{\circ} \cdot 3\frac{16}{113} \cdot 2}\\\\r=4\frac{55}{71}m \\\\ \small \begin{array}{|l|} \hline b=\\ \hline 7\frac{1}{2} m \\ \hline 75 dm \\ \hline 750 cm \\ \hline 7,5\cdot 10^{3} mm \\ \hline 7,5\cdot 10^{6} \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 r=\\ \hline 4\frac{55}{71} m \\ \hline 47,7 dm \\ \hline 477 cm \\ \hline 4,77\cdot 10^{3} mm \\ \hline 4774648\frac{2}{9} \mu m \\ \hline \end{array}$