Geometrie-Stereometrie-Quader


  • $V = a\cdot b\cdot c$
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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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    $c = \sqrt{d^{2} -b^{2} -a^{2} }$
    1 2

Beispiel Nr: 01
$ \text{Gegeben:}\\\text{Höhe} \qquad c \qquad [m] \\ \text{Breite} \qquad b \qquad [m] \\ \text{Oberfläche} \qquad O \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Länge} \qquad a \qquad [m] \\ \\ a = \frac{O-2\cdot b\cdot c}{2\cdot (b+c)}\\ \textbf{Gegeben:} \\ c=2m \qquad b=7m \qquad O=2m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ a = \frac{O-2\cdot b\cdot c}{2\cdot (b+c)} \\ c=2m\\ b=7m\\ O=2m^{2}\\ a = \frac{2m^{2}-2\cdot 7m\cdot 2m}{2\cdot (7m+2m)}\\\\a=-1\frac{4}{9}m \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 2 m \\ \hline 20 dm \\ \hline 200 cm \\ \hline 2\cdot 10^{3} mm \\ \hline 2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline O=\\ \hline 2 m^2 \\ \hline 200 dm^2 \\ \hline 2\cdot 10^{4} cm^2 \\ \hline 2\cdot 10^{6} mm^2 \\ \hline \frac{1}{50} a \\ \hline 0,0002 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline -1\frac{4}{9} m \\ \hline -14\frac{4}{9} dm \\ \hline -144\frac{4}{9} cm \\ \hline -1444\frac{4}{9} mm \\ \hline -1444444\frac{4}{9} \mu m \\ \hline \end{array}$