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$ V = r^{2} \cdot \pi \cdot h $
$ r = \sqrt{\frac{ V}{\pi \cdot h}} $
$ h = \frac{ V}{r^{2} \cdot \pi } $
$ O = 2\cdot r\cdot \pi \cdot (r+h) $
$ r = 0,5\cdot (-h+\sqrt{h^{2} +\frac{O}{\pi }}) $
$ h = \frac{0-2\cdot \pi \cdot r^{2} }{ 2\cdot r\cdot \pi } $
Geometrie-Stereometrie-Kreiszylinder
$V = r^{2} \cdot \pi \cdot h$
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2
$r = \sqrt{\frac{ V}{\pi \cdot h}}$
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$h = \frac{ V}{r^{2} \cdot \pi }$
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$O = 2\cdot r\cdot \pi \cdot (r+h)$
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2
$r = 0,5\cdot (-h+\sqrt{h^{2} +\frac{O}{\pi }})$
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$h = \frac{0-2\cdot \pi \cdot r^{2} }{ 2\cdot r\cdot \pi }$
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Beispiel Nr: 01
$\begin{array}{l}
\text{Gegeben:}\\\text{Kreiszahl} \qquad \pi \qquad [] \\
\text{Radius} \qquad r \qquad [m] \\
\text{Oberfläche} \qquad O \qquad [m^{2}] \\
\\ \text{Gesucht:} \\\text{Körperhöhe} \qquad h \qquad [m] \\
\\ h = \frac{0-2\cdot \pi \cdot r^{2} }{ 2\cdot r\cdot \pi }\\ \textbf{Gegeben:} \\ \pi=4 \qquad r=3\frac{16}{113}m \qquad O=50m^{2} \qquad \\ \\ \textbf{Rechnung:} \\
h = \frac{0-2\cdot \pi \cdot r^{2} }{ 2\cdot r\cdot \pi } \\
\pi=4\\
r=3\frac{16}{113}m\\
O=50m^{2}\\
h = \frac{0-2\cdot 4 \cdot (3\frac{16}{113}m)^{2} }{ 2\cdot 3\frac{16}{113}m\cdot \pi }\\\\h=-1,15m
\\\\ \small \begin{array}{|l|} \hline r=\\ \hline 3\frac{16}{113} m \\ \hline 31,4 dm \\ \hline 314 cm \\ \hline 3,14\cdot 10^{3} mm \\ \hline 3141592\frac{7}{10} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline O=\\ \hline 50 m^2 \\ \hline 5\cdot 10^{3} dm^2 \\ \hline 5\cdot 10^{5} cm^2 \\ \hline 5\cdot 10^{7} mm^2 \\ \hline \frac{1}{2} a \\ \hline 0,005 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\ \hline -1,15 m \\ \hline -11,5 dm \\ \hline -115 cm \\ \hline -1,15\cdot 10^{3} mm \\ \hline -1,15\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$