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: 01
$ \text{Gegeben:}\\\text{Mantelfläche} \qquad M \qquad [m^{2}] \\ \text{Grundfläche} \qquad G \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Oberfläche} \qquad O \qquad [m^{2}] \\ \\ O = 2\cdot G +M \\ \textbf{Gegeben:} \\ M=3m^{2} \qquad G=5m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ O = 2\cdot G +M \\ M=3m^{2}\\ G=5m^{2}\\ O = 2 \cdot 5m^{2} + 3m^{2}\\\\ O=13m^{2} \\\\\\ \small \begin{array}{|l|} \hline M=\\ \hline 3 m^2 \\ \hline 300 dm^2 \\ \hline 3\cdot 10^{4} cm^2 \\ \hline 3\cdot 10^{6} mm^2 \\ \hline \frac{3}{100} a \\ \hline 0,0003 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline 5 m^2 \\ \hline 500 dm^2 \\ \hline 5\cdot 10^{4} cm^2 \\ \hline 5\cdot 10^{6} mm^2 \\ \hline \frac{1}{20} a \\ \hline 0,0005 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline O=\\ \hline 13 m^2 \\ \hline 1,3\cdot 10^{3} dm^2 \\ \hline 1,3\cdot 10^{5} cm^2 \\ \hline 1,3\cdot 10^{7} mm^2 \\ \hline \frac{13}{100} a \\ \hline 0,0013 ha \\ \hline \end{array}$