Geometrie-Stereometrie-Quader


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

Beispiel Nr: 02
$ \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=2m \qquad b=7m \qquad d=12m \qquad \\ \\ \textbf{Rechnung:} \\ c = \sqrt{d^{2} -b^{2} -a^{2} } \\ a=2m\\ b=7m\\ d=12m\\ c = \sqrt{(12m)^{2} -(7m)^{2} -(2m)^{2} }\\\\c=9,54m \\\\\\ \small \begin{array}{|l|} \hline a=\\ \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 d=\\ \hline 12 m \\ \hline 120 dm \\ \hline 1,2\cdot 10^{3} cm \\ \hline 1,2\cdot 10^{4} mm \\ \hline 1,2\cdot 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline c=\\ \hline 9,54 m \\ \hline 95,4 dm \\ \hline 954 cm \\ \hline 9,54\cdot 10^{3} mm \\ \hline 9,54\cdot 10^{6} \mu m \\ \hline \end{array}$