$V = a\cdot b\cdot c$
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$a = \frac{ V}{b\cdot c}$
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$b = \frac{ V}{a\cdot c}$
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$c = \frac{ V}{b\cdot a}$
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$O = 2\cdot (a\cdot b + a\cdot c + b\cdot c)$
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$a = \frac{O-2\cdot b\cdot c}{2\cdot (b+c)}$
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$b = \frac{O-2\cdot a\cdot c}{2\cdot (a+c)}$
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$c = \frac{O-2\cdot b\cdot a}{2\cdot (b+a)}$
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$d = \sqrt{a^{2} +b^{2} +c^{2} }$
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$a = \sqrt{d^{2} -b^{2} -c^{2} }$
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$b = \sqrt{d^{2} -a^{2} -c^{2} }$
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$c = \sqrt{d^{2} -b^{2} -a^{2} }$
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Beispiel Nr: 01
$\begin{array}{l} \text{Gegeben:}\\\text{Volumen} \qquad V \qquad [m^{3}] \\ \text{Länge} \qquad a \qquad [m] \\ \text{Breite} \qquad b \qquad [m] \\ \\ \text{Gesucht:} \\\text{Höhe} \qquad c \qquad [m] \\ \\ c = \frac{ V}{b\cdot a}\\ \textbf{Gegeben:} \\ V=3m^{3} \qquad a=6m \qquad b=5m \qquad \\ \\ \textbf{Rechnung:} \\ c = \frac{ V}{b\cdot a} \\ V=3m^{3}\\ a=6m\\ b=5m\\ c = \frac{ 3m^{3}}{5m\cdot 6m}\\\\c=\frac{1}{10}m \\\\\\ \small \begin{array}{|l|} \hline V=\\ \hline 3 m^3 \\ \hline 3\cdot 10^{3} dm^3 \\ \hline 3\cdot 10^{6} cm^3 \\ \hline 3\cdot 10^{9} mm^3 \\ \hline 3\cdot 10^{3} l \\ \hline 30 hl \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline \frac{1}{10} m \\ \hline 1 dm \\ \hline 10 cm \\ \hline 100 mm \\ \hline 10^{5} \mu m \\ \hline \end{array} \end{array}$