Geometrie-Stereometrie-Prisma


  • $V = G\cdot h$
    1 2
    $G = \frac{V}{h}$
    1 2
    $h = \frac{V}{G}$
    1 2
    $O = 2\cdot G +M $
    1 2 3
    $G = \frac{O-M}{2}$
    1 2
    $M = O- 2\cdot G $
    1 2 3

Beispiel Nr: 03
$ \text{Gegeben:}\\\text{Oberfläche} \qquad O \qquad [m^{2}] \\ \\\text{Grundfläche} \qquad G \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Mantelfläche} \qquad M \qquad [m^{2}] \\ \\ M = O- 2\cdot G \\ \textbf{Gegeben:} \\ O=1,2\cdot 10^{3}m^{2} \qquad G=300m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ M = O- 2\cdot G \\ O=1,2\cdot 10^{3}m^{2}\\ G=300m^{2}\\ M = 1,2\cdot 10^{3}m^{2}- 2\cdot300m^{2} \\ M=600m^{2} \\\\\\ \small \begin{array}{|l|} \hline O=\\ \hline 1,2\cdot 10^{3} m^2 \\ \hline 1,2\cdot 10^{5} dm^2 \\ \hline 1,2\cdot 10^{7} cm^2 \\ \hline 1,2\cdot 10^{9} mm^2 \\ \hline 12 a \\ \hline \frac{3}{25} ha \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline 300 m^2 \\ \hline 3\cdot 10^{4} dm^2 \\ \hline 3\cdot 10^{6} cm^2 \\ \hline 3\cdot 10^{8} mm^2 \\ \hline 3 a \\ \hline \frac{3}{100} ha \\ \hline \end{array} \small \begin{array}{|l|} \hline M=\\ \hline 600 m^2 \\ \hline 6\cdot 10^{4} dm^2 \\ \hline 6\cdot 10^{6} cm^2 \\ \hline 6\cdot 10^{8} mm^2 \\ \hline 6 a \\ \hline \frac{3}{50} ha \\ \hline \end{array}$