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$ V = (r_{1} ^{2} - r_{2} ^{2} )\cdot \pi \cdot h $
$ r_{1} = \sqrt{\frac{ V}{\pi \cdot h}+r_{2} ^{2} } $
$ r_{2} = \sqrt{r_{1} ^{2} - \frac{ V}{\pi \cdot h}} $
$ h = \frac{ V}{(r_{1} ^{2} - r_{2} ^{2} )\cdot \pi } $
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: 01
$\begin{array}{l}
\text{Gegeben:}\\\text{Körperhöhe} \qquad h \qquad [m] \\
\text{Kreiszahl} \qquad \pi \qquad [] \\
\text{Radius 2} \qquad r_{2} \qquad [m] \\
\text{Volumen} \qquad V \qquad [m^{3}] \\
\\ \text{Gesucht:} \\\text{Radius 1} \qquad r_{1} \qquad [m] \\
\\ r_{1} = \sqrt{\frac{ V}{\pi \cdot h}+r_{2} ^{2} }\\ \textbf{Gegeben:} \\ h=4m \qquad \pi=3\frac{16}{113} \qquad r_{2}=5m \qquad V=6m^{3} \qquad \\ \\ \textbf{Rechnung:} \\
r_{1} = \sqrt{\frac{ V}{\pi \cdot h}+r_{2} ^{2} } \\
h=4m\\
\pi=3\frac{16}{113}\\
r_{2}=5m\\
V=6m^{3}\\
r_{1} = \sqrt{\frac{ 6m^{3}}{3\frac{16}{113} \cdot 4m}+5m ^{2} }\\\\r_{1}=5,05m
\\\\\\ \small \begin{array}{|l|} \hline h=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline r2=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline V=\\ \hline 6 m^3 \\ \hline 6\cdot 10^{3} dm^3 \\ \hline 6\cdot 10^{6} cm^3 \\ \hline 6\cdot 10^{9} mm^3 \\ \hline 6\cdot 10^{3} l \\ \hline 60 hl \\ \hline \end{array}\\ \small \begin{array}{|l|} \hline r1=\\ \hline 5,05 m \\ \hline 50,5 dm \\ \hline 504\frac{91}{121} cm \\ \hline 5047\frac{63}{121} mm \\ \hline 5,05\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$