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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
$\begin{array}{l}
\text{Gegeben:}\\\text{Kreiszahl} \qquad \pi \qquad [] \\
\text{Volumen} \qquad V \qquad [m^{3}] \\
\text{Radius} \qquad r \qquad [m] \\
\\ \text{Gesucht:} \\\text{Körperhöhe} \qquad h \qquad [m] \\
\\ h = \frac{ V}{r^{2} \cdot \pi }\\ \textbf{Gegeben:} \\ \pi=3\frac{16}{113} \qquad V=4m^{3} \qquad r=2m \qquad \\ \\ \textbf{Rechnung:} \\
h = \frac{ V}{r^{2} \cdot \pi } \\
\pi=3\frac{16}{113}\\
V=4m^{3}\\
r=2m\\
h = \frac{ 4m^{3}}{(2m)^{2} \cdot 3\frac{16}{113} }\\\\h=0,318m
\\\\ \small \begin{array}{|l|} \hline V=\\ \hline 4 m^3 \\ \hline 4\cdot 10^{3} dm^3 \\ \hline 4\cdot 10^{6} cm^3 \\ \hline 4\cdot 10^{9} mm^3 \\ \hline 4\cdot 10^{3} l \\ \hline 40 hl \\ \hline \end{array} \small \begin{array}{|l|} \hline r=\\ \hline 2 m \\ \hline 20 dm \\ \hline 200 cm \\ \hline 2\cdot 10^{3} mm \\ \hline 2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\ \hline 0,318 m \\ \hline 3\frac{13}{71} dm \\ \hline 31,8 cm \\ \hline 318 mm \\ \hline 3,18\cdot 10^{5} \mu m \\ \hline \end{array} \end{array}$