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: 01
$\begin{array}{l} \text{Gegeben:}\\\text{Oberfläche} \qquad O \qquad [m^{2}] \\ \\\text{Mantelfläche} \qquad M \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Grundfläche} \qquad G \qquad [m^{2}] \\ \\ G = O-M\\ \textbf{Gegeben:} \\ O=5m^{2} \qquad M=6m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ G = O-M \\ M=6m^{2}\\ O=5m^{2}\\ G =5m^{2}-6m^{2}\\\ G=-1m^{2} \\\\\\ \small \begin{array}{|l|} \hline O=\\ \hline 5 m^2 \\ \hline 500 dm^2 \\ \hline 5\cdot 10^{4} cm^2 \\ \hline 5\cdot 10^{6} mm^2 \\ \hline \frac{1}{20} a \\ \hline 0,0005 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline M=\\ \hline 6 m^2 \\ \hline 600 dm^2 \\ \hline 6\cdot 10^{4} cm^2 \\ \hline 6\cdot 10^{6} mm^2 \\ \hline \frac{3}{50} a \\ \hline 0,0006 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline -1 m^2 \\ \hline -100 dm^2 \\ \hline -10^{4} cm^2 \\ \hline -10^{6} mm^2 \\ \hline -\frac{1}{100} a \\ \hline -0,0001 ha \\ \hline \end{array} \end{array}$