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{Mantelfläche} \qquad M \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Grundfläche} \qquad G \qquad [m^{2}] \\ \\ G = \frac{O-M}{2}\\ \textbf{Gegeben:} \\ O=540m^{2} \qquad M=30m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ G = \frac{O-M}{2} \\ M=30m^{2}\\ O=540m^{2}\\ G = \frac{540m^{2}-30m^{2}}{2}\\\ G=255m^{2} \\\\\\ \small \begin{array}{|l|} \hline O=\\ \hline 540 m^2 \\ \hline 5,4\cdot 10^{4} dm^2 \\ \hline 5,4\cdot 10^{6} cm^2 \\ \hline 5,4\cdot 10^{8} mm^2 \\ \hline 5\frac{2}{5} a \\ \hline 0,054 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline M=\\ \hline 30 m^2 \\ \hline 3\cdot 10^{3} dm^2 \\ \hline 3\cdot 10^{5} cm^2 \\ \hline 3\cdot 10^{7} mm^2 \\ \hline \frac{3}{10} a \\ \hline 0,003 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline 255 m^2 \\ \hline 2,55\cdot 10^{4} dm^2 \\ \hline 2,55\cdot 10^{6} cm^2 \\ \hline 2,55\cdot 10^{8} mm^2 \\ \hline 2\frac{11}{20} a \\ \hline 0,0255 ha \\ \hline \end{array}$