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{Volumen} \qquad V \qquad [m^{3}] \\ \text{Grundfläche} \qquad G \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Körperhöhe} \qquad h \qquad [m] \\ \\ h = \frac{V}{G}\\ \textbf{Gegeben:} \\ V=5m^{3} \qquad G=6m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ h = \frac{V}{G} \\ V=5m^{3}\\ G=6m^{2}\\ h = \frac{5m^{3}}{6m^{2}}\\\\h=\frac{5}{6}m \\\\\\ \small \begin{array}{|l|} \hline V=\\ \hline 5 m^3 \\ \hline 5\cdot 10^{3} dm^3 \\ \hline 5\cdot 10^{6} cm^3 \\ \hline 5\cdot 10^{9} mm^3 \\ \hline 5\cdot 10^{3} l \\ \hline 50 hl \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline 6 m^2 \\ \hline 600 dm^2 \\ \hline 6\cdot 10^{4} cm^2 \\ \hline 6\cdot 10^{6} mm^2 \\ \hline \frac{3}{50} a \\ \hline 0,0006 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\ \hline \frac{5}{6} m \\ \hline 8\frac{1}{3} dm \\ \hline 83\frac{1}{3} cm \\ \hline 833\frac{1}{3} mm \\ \hline 833333\frac{1}{3} \mu m \\ \hline \end{array}$