Geometrie-Stereometrie-Hohlzylinder


  • $V = (r_{1} ^{2} - r_{2} ^{2} )\cdot \pi \cdot h$
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    $r_{1} = \sqrt{\frac{ V}{\pi \cdot h}+r_{2} ^{2} }$
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    $r_{2} = \sqrt{r_{1} ^{2} - \frac{ V}{\pi \cdot h}}$
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    $h = \frac{ V}{(r_{1} ^{2} - r_{2} ^{2} )\cdot \pi }$
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Beispiel Nr: 02
$ \text{Gegeben:}\\\text{Körperhöhe} \qquad h \qquad [m] \\ \text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Radius 2} \qquad r_{2} \qquad [m] \\ \text{Radius 1} \qquad r_{1} \qquad [m] \\ \\ \text{Gesucht:} \\\text{Volumen} \qquad V \qquad [m^{3}] \\ \\ V = (r_{1} ^{2} - r_{2} ^{2} )\cdot \pi \cdot h\\ \textbf{Gegeben:} \\ h=6m \qquad \pi=3\frac{16}{113} \qquad r_{2}=4m \qquad r_{1}=8m \qquad \\ \\ \textbf{Rechnung:} \\ V = (r_{1} ^{2} - r_{2} ^{2} )\cdot \pi \cdot h \\ h=6m\\ \pi=3\frac{16}{113}\\ r_{2}=4m\\ r_{1}=8m\\ V = (8m ^{2} - 4m ^{2} )\cdot 3\frac{16}{113} \cdot 6m\\\\V=905m^{3} \\\\\\ \small \begin{array}{|l|} \hline h=\\ \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 r2=\\ \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 r1=\\ \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 V=\\ \hline 905 m^3 \\ \hline 9,05\cdot 10^{5} dm^3 \\ \hline 904778697\frac{3}{5} cm^3 \\ \hline 9,05\cdot 10^{11} mm^3 \\ \hline 9,05\cdot 10^{5} l \\ \hline 9,05\cdot 10^{3} hl \\ \hline \end{array}$