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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    $c = \sqrt{d^{2} -b^{2} -a^{2} }$
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Beispiel Nr: 01
$ \text{Gegeben:}\\\text{Länge} \qquad a \qquad [m] \\ \text{Breite} \qquad b \qquad [m] \\ \text{Raumdiagonale} \qquad d \qquad [m] \\ \\ \text{Gesucht:} \\\text{Höhe} \qquad c \qquad [m] \\ \\ c = \sqrt{d^{2} -b^{2} -a^{2} }\\ \textbf{Gegeben:} \\ a=1m \qquad b=4m \qquad d=8m \qquad \\ \\ \textbf{Rechnung:} \\ c = \sqrt{d^{2} -b^{2} -a^{2} } \\ a=1m\\ b=4m\\ d=8m\\ c = \sqrt{(8m)^{2} -(4m)^{2} -(1m)^{2} }\\\\c=6,86m \\\\\\ \small \begin{array}{|l|} \hline a=\\ \hline 1 m \\ \hline 10 dm \\ \hline 100 cm \\ \hline 10^{3} mm \\ \hline 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline b=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline d=\\ \hline 8 m \\ \hline 80 dm \\ \hline 800 cm \\ \hline 8\cdot 10^{3} mm \\ \hline 8\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 6,86 m \\ \hline 68,6 dm \\ \hline 686 cm \\ \hline 6,86\cdot 10^{3} mm \\ \hline 6,86\cdot 10^{6} \mu m \\ \hline \end{array}$