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
$\text{Gegeben:}\\\text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Radius (außerer Kreis)} \qquad r_{a} \qquad [m] \\ \text{Radius (innerer Kreis)} \qquad r_{i} \qquad [m] \\ \\ \text{Gesucht:} \\\text{Fläche} \qquad A \qquad [m^{2}] \\ \\ A = (r_{a} ^{2} - r_{i} ^{2} )\cdot\pi\\ \textbf{Gegeben:} \\ \pi=3\frac{16}{113} \qquad r_{a}=14m \qquad r_{i}=6m \qquad \\ \\ \textbf{Rechnung:} \\ A = (r_{a} ^{2} - r_{i} ^{2} )\cdot \pi \\ \pi=3\frac{16}{113}\\ r_{a}=14m\\ r_{i}=6m\\ A = (14m ^{2} - 6m ^{2} )\cdot 3\frac{16}{113}\\\\A=503m^{2} \\\\ \small \begin{array}{|l|} \hline ra=\\ \hline 14 m \\ \hline 140 dm \\ \hline 1,4\cdot 10^{3} cm \\ \hline 1,4\cdot 10^{4} mm \\ \hline 1,4\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline ri=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 503 m^2 \\ \hline 5,03\cdot 10^{4} dm^2 \\ \hline 5026548\frac{8}{25} cm^2 \\ \hline 5,03\cdot 10^{8} mm^2 \\ \hline 5\frac{3}{113} a \\ \hline 0,0503 ha \\ \hline \end{array}$