Geometrie-Stereometrie-Pyramide

$V =\frac{1}{3} G\cdot h$
1 2 3 4
$G = \frac{3 \cdot V}{h}$
1 2
$h = \frac{3 \cdot V}{G}$
1 2 3
$O = G +M$
1 2
$G = O-M$
1 2 3
$M = O- G$
1 2
$\text{Rechteckige Pyramide}$
1 2 3 4 5 6 7 8 9 10 11
$\text{Quadratische Pyramide}$
1 2 3 4 5 6 7 8 9 10 11 12 13
Beispiel Nr: 03
$\begin{array}{l} \text{Gegeben:}\\\text{Körperhöhe} \qquad h \qquad [m] \\ \text{Grundfläche} \qquad G \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Volumen} \qquad V \qquad [m^{3}] \\ \\ V =\frac{1}{3} G\cdot h\\ \textbf{Gegeben:} \\ h=1\frac{2}{5}m \qquad G=6m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ V = \frac{1}{3} \cdot G\cdot h \\ h=1\frac{2}{5}m\\ G=6m^{2}\\ V = \frac{1}{3}6m^{2}\cdot 1\frac{2}{5}m\\\\V=2\frac{4}{5}m^{3} \\\\\\ \small \begin{array}{|l|} \hline h=\\ \hline 1\frac{2}{5} m \\ \hline 14 dm \\ \hline 140 cm \\ \hline 1,4\cdot 10^{3} mm \\ \hline 1,4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline 6 m^2 \\ \hline 600 dm^2 \\ \hline 6\cdot 10^{4} cm^2 \\ \hline 6\cdot 10^{6} mm^2 \\ \hline \frac{3}{50} a \\ \hline 0,0006 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline V=\\ \hline 2\frac{4}{5} m^3 \\ \hline 2,8\cdot 10^{3} dm^3 \\ \hline 2,8\cdot 10^{6} cm^3 \\ \hline 2,8\cdot 10^{9} mm^3 \\ \hline 2,8\cdot 10^{3} l \\ \hline 28 hl \\ \hline \end{array} \end{array}$