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{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=3m^{3} \qquad G=1m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ h = \frac{V}{G} \\ V=3m^{3}\\ G=1m^{2}\\ h = \frac{3m^{3}}{1m^{2}}\\\\h=3m \\\\\\ \small \begin{array}{|l|} \hline V=\\ \hline 3 m^3 \\ \hline 3\cdot 10^{3} dm^3 \\ \hline 3\cdot 10^{6} cm^3 \\ \hline 3\cdot 10^{9} mm^3 \\ \hline 3\cdot 10^{3} l \\ \hline 30 hl \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline 1 m^2 \\ \hline 100 dm^2 \\ \hline 10^{4} cm^2 \\ \hline 10^{6} mm^2 \\ \hline \frac{1}{100} a \\ \hline 0,0001 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\ \hline 3 m \\ \hline 30 dm \\ \hline 300 cm \\ \hline 3\cdot 10^{3} mm \\ \hline 3\cdot 10^{6} \mu m \\ \hline \end{array}$