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$ V = \frac{1}{3}\cdot r^{2} \cdot \pi \cdot h $
$ r = \sqrt{\frac{3\cdot V}{\pi \cdot h}} $
$ h = \frac{3\cdot V}{r^{2} \cdot \pi } $
$ O = r\cdot \pi \cdot (r+s) $
$ s = \frac{ O}{r\cdot \pi } - r $
$ r = \frac{-\pi \cdot s + \sqrt{(\pi \cdot s)^{2} +4\cdot \pi \cdot O}}{ 2\cdot \pi } $
$ M = r\cdot \pi \cdot s $
$ s = \frac{ M}{r\cdot \pi } $
$ r = \frac{ M}{s\cdot \pi } $
$ s =\sqrt{h^{2} + r^{2} } $
$ r =\sqrt{s^{2} - h^{2} } $
$ h =\sqrt{s^{2} - r^{2} } $
Geometrie-Stereometrie-Kreiskegel
$V = \frac{1}{3}\cdot r^{2} \cdot \pi \cdot h$
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$r = \sqrt{\frac{3\cdot V}{\pi \cdot h}}$
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$h = \frac{3\cdot V}{r^{2} \cdot \pi }$
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$O = r\cdot \pi \cdot (r+s)$
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$s = \frac{ O}{r\cdot \pi } - r$
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$r = \frac{-\pi \cdot s + \sqrt{(\pi \cdot s)^{2} +4\cdot \pi \cdot O}}{ 2\cdot \pi }$
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$M = r\cdot \pi \cdot s$
$s = \frac{ M}{r\cdot \pi }$
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$r = \frac{ M}{s\cdot \pi }$
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$s =\sqrt{h^{2} + r^{2} }$
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$r =\sqrt{s^{2} - h^{2} }$
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$h =\sqrt{s^{2} - r^{2} }$
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Beispiel Nr: 01
$\begin{array}{l}
\text{Gegeben:}\\\text{Mantellinie} \qquad s \qquad [m]\\
\text{Radius} \qquad r \qquad [m] \\
\\ \text{Gesucht:} \\ \text{Höhe} \qquad h \qquad [m] \\
\\ h =\sqrt{s^{2} - r^{2} }\\ \textbf{Gegeben:} \\ s=6m \qquad r=4m \qquad \\ \\ \textbf{Rechnung:} \\
h =\sqrt{s^{2} - r^{2} } \\
s=6m\\
r=4m\\
h =\sqrt{(6m)^{2} - (4m)^{2} }\\\\h=4,47m
\\\\\\ \small \begin{array}{|l|} \hline r=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline s=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\ \hline 4,47 m \\ \hline 44,7 dm \\ \hline 447 cm \\ \hline 4,47\cdot 10^{3} mm \\ \hline 4,47\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$