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{Körperhöhe} \qquad h \qquad [m] \\ \text{Volumen} \qquad V \qquad [m^{3}] \\ \\ \text{Gesucht:} \\\text{Grundfläche} \qquad G \qquad [m^{2}] \\ \\ G = \frac{V}{h}\\ \textbf{Gegeben:} \\ h=4m \qquad V=5m^{3} \qquad \\ \\ \textbf{Rechnung:} \\ G = \frac{V}{h} \\ h=4m\\ V=5m^{3}\\ G = \frac{5m^{3}}{4m}\\\\G=1\frac{1}{4}m^{2} \\\\\\ \small \begin{array}{|l|} \hline h=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \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 1\frac{1}{4} m^2 \\ \hline 125 dm^2 \\ \hline 1,25\cdot 10^{4} cm^2 \\ \hline 1,25\cdot 10^{6} mm^2 \\ \hline \frac{1}{80} a \\ \hline 0,000125 ha \\ \hline \end{array}$