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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    $c = \frac{ V}{b\cdot a}$
    1 2
    $O = 2\cdot (a\cdot b + a\cdot c + b\cdot c)$
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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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    $b = \sqrt{d^{2} -a^{2} -c^{2} }$
    1 2
    $c = \sqrt{d^{2} -b^{2} -a^{2} }$
    1 2

Beispiel Nr: 01
$ \text{Gegeben:}\\\text{Höhe} \qquad c \qquad [m] \\ \text{Breite} \qquad b \qquad [m] \\ \text{Volumen} \qquad V \qquad [m^{3}] \\ \\ \text{Gesucht:} \\\text{Länge} \qquad a \qquad [m] \\ \\ a = \frac{ V}{b\cdot c}\\ \textbf{Gegeben:} \\ c=2m \qquad b=6m \qquad V=5m^{3} \qquad \\ \\ \textbf{Rechnung:} \\ a = \frac{ V}{b\cdot c} \\ c=2m\\ b=6m\\ V=5m^{3}\\ a = \frac{ 5m^{3}}{6m\cdot 2m}\\\\a=\frac{5}{12}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 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 V=\\ \hline 5 m^3 \\ \hline 5\cdot 10^{3} dm^3 \\ \hline 5\cdot 10^{6} cm^3 \\ \hline 5\cdot 10^{9} mm^3 \\ \hline 5\cdot 10^{3} l \\ \hline 50 hl \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline \frac{5}{12} m \\ \hline 4\frac{1}{6} dm \\ \hline 41\frac{2}{3} cm \\ \hline 416\frac{2}{3} mm \\ \hline 416666\frac{2}{3} \mu m \\ \hline \end{array}$