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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: 02
$\begin{array}{l}
\text{Gegeben:}\\\text{Körperhöhe} \qquad h \qquad [m] \\
\text{Kreiszahl} \qquad \pi \qquad [] \\
\text{Radius} \qquad r \qquad [m] \\
\\ \text{Gesucht:} \\\text{Oberfläche} \qquad O \qquad [m^{2}] \\
\\ O = 2\cdot r\cdot \pi \cdot (r+h)\\ \textbf{Gegeben:} \\ h=5m \qquad \pi=3\frac{16}{113} \qquad r=10m \qquad \\ \\ \textbf{Rechnung:} \\
O = 2\cdot r\cdot \pi \cdot (r+h) \\
h=5m\\
\pi=3\frac{16}{113}\\
r=10m\\
O = 2 \cdot 10m\cdot 3\frac{16}{113} \cdot (10m+5m)\\\\O=942m^{2}
\\\\\\ \small \begin{array}{|l|} \hline h=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline r=\\ \hline 10 m \\ \hline 100 dm \\ \hline 10^{3} cm \\ \hline 10^{4} mm \\ \hline 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline O=\\ \hline 942 m^2 \\ \hline 9,42\cdot 10^{4} dm^2 \\ \hline 9424778\frac{1}{10} cm^2 \\ \hline 9,42\cdot 10^{8} mm^2 \\ \hline 9\frac{48}{113} a \\ \hline 0,0942 ha \\ \hline \end{array} \end{array}$