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$ V = G\cdot h $
$ G = \frac{V}{h} $
$ h = \frac{V}{G} $
$ O = 2\cdot G +M $
$ G = \frac{O-M}{2} $
$ M = O- 2\cdot G $
Geometrie-Stereometrie-Prisma
$V = G\cdot h$
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2
$G = \frac{V}{h}$
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$h = \frac{V}{G}$
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2
$O = 2\cdot G +M $
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$G = \frac{O-M}{2}$
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$M = O- 2\cdot G $
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Beispiel Nr: 03
$\begin{array}{l}
\text{Gegeben:}\\\text{Mantelfläche} \qquad M \qquad [m^{2}] \\
\text{Grundfläche} \qquad G \qquad [m^{2}] \\
\\ \text{Gesucht:} \\\text{Oberfläche} \qquad O \qquad [m^{2}] \\
\\ O = 2\cdot G +M \\ \textbf{Gegeben:} \\ M=3m^{2} \qquad G=5m^{2} \qquad \\ \\ \textbf{Rechnung:} \\
O = 2\cdot G +M \\
M=3m^{2}\\
G=5m^{2}\\
O = 2 \cdot 5m^{2} + 3m^{2}\\\\
O=13m^{2}
\\\\\\ \small \begin{array}{|l|} \hline M=\\ \hline 3 m^2 \\ \hline 300 dm^2 \\ \hline 3\cdot 10^{4} cm^2 \\ \hline 3\cdot 10^{6} mm^2 \\ \hline \frac{3}{100} a \\ \hline 0,0003 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline G=\\ \hline 5 m^2 \\ \hline 500 dm^2 \\ \hline 5\cdot 10^{4} cm^2 \\ \hline 5\cdot 10^{6} mm^2 \\ \hline \frac{1}{20} a \\ \hline 0,0005 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline O=\\ \hline 13 m^2 \\ \hline 1,3\cdot 10^{3} dm^2 \\ \hline 1,3\cdot 10^{5} cm^2 \\ \hline 1,3\cdot 10^{7} mm^2 \\ \hline \frac{13}{100} a \\ \hline 0,0013 ha \\ \hline \end{array} \end{array}$