Geometrie-Kreis-Kreisring


  • $A = (r_{a} ^{2} - r_{i} ^{2} )\cdot\pi$
    1 2 3
    $r_{a} = \sqrt{\frac{A}{\pi } + r_{i} ^{2} }$
    1
    $r_{i} = \sqrt{r_{a} ^{2} - \frac{A}{\pi } }$
    1

Beispiel Nr: 01
$ \text{Gegeben:}\\\text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Fläche} \qquad A \qquad [m^{2}] \\ \text{Radius (innerer Kreis)} \qquad r_{i} \qquad [m] \\ \\ \text{Gesucht:} \\\text{Radius (außerer Kreis)} \qquad r_{a} \qquad [m] \\ \\ r_{a} = \sqrt{\frac{A}{\pi } + r_{i} ^{2} }\\ \textbf{Gegeben:} \\ \pi=3\frac{16}{113} \qquad A=4m^{2} \qquad r_{i}=6m \qquad \\ \\ \textbf{Rechnung:} \\ r_{a} = \sqrt{\frac{A}{\pi } + r_{i} ^{2} } \\ \pi=3\frac{16}{113}\\ A=4m^{2}\\ r_{i}=6m\\ r_{a} = \sqrt{\frac{4m^{2}}{3\frac{16}{113} } + 6m ^{2} }\\\\r_{a}=6,11m \\\\ \small \begin{array}{|l|} \hline A=\\ \hline 4 m^2 \\ \hline 400 dm^2 \\ \hline 4\cdot 10^{4} cm^2 \\ \hline 4\cdot 10^{6} mm^2 \\ \hline \frac{1}{25} a \\ \hline 0,0004 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline ri=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline ra=\\ \hline 6,11 m \\ \hline 61,1 dm \\ \hline 611 cm \\ \hline 6,11\cdot 10^{3} mm \\ \hline 6,11\cdot 10^{6} \mu m \\ \hline \end{array}$