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: 02
$ \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=4\frac{1}{5}m^{2} \qquad G=1\frac{1}{5}m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ M = O- 2\cdot G \\ O=4\frac{1}{5}m^{2}\\ G=1\frac{1}{5}m^{2}\\ M = 4\frac{1}{5}m^{2}- 2\cdot1\frac{1}{5}m^{2} \\ M=1\frac{4}{5}m^{2} \\\\\\ \small \begin{array}{|l|} \hline O=\\ \hline 4\frac{1}{5} m^2 \\ \hline 420 dm^2 \\ \hline 4,2\cdot 10^{4} cm^2 \\ \hline 4,2\cdot 10^{6} mm^2 \\ \hline 0,042 a \\ \hline 0,00042 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline 1\frac{1}{5} m^2 \\ \hline 120 dm^2 \\ \hline 1,2\cdot 10^{4} cm^2 \\ \hline 1,2\cdot 10^{6} mm^2 \\ \hline 0,012 a \\ \hline 0,00012 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline M=\\ \hline 1\frac{4}{5} m^2 \\ \hline 180 dm^2 \\ \hline 1,8\cdot 10^{4} cm^2 \\ \hline 1,8\cdot 10^{6} mm^2 \\ \hline 0,018 a \\ \hline 0,00018 ha \\ \hline \end{array}$