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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
$\begin{array}{l}
\text{Gegeben:}\\\text{Körperhöhe} \qquad h \qquad [m] \\
\text{Kreiszahl} \qquad \pi \qquad [] \\
\text{Volumen} \qquad V \qquad [m^{3}] \\
\text{Radius 1} \qquad r_{1} \qquad [m] \\
\\ \text{Gesucht:} \\\text{Radius 2} \qquad r_{2} \qquad [m] \\
\\ r_{2} = \sqrt{r_{1} ^{2} - \frac{ V}{\pi \cdot h}}\\ \textbf{Gegeben:} \\ h=4m \qquad \pi=3\frac{16}{113} \qquad V=2m^{3} \qquad r_{1}=6m \qquad \\ \\ \textbf{Rechnung:} \\
r_{2} = \sqrt{r_{1} ^{2} - \frac{ V}{\pi \cdot h}} \\
h=4m\\
\pi=3\frac{16}{113}\\
V=2m^{3}\\
r_{1}=6m\\
r_{2} = \sqrt{6m ^{2} - \frac{ 2m^{3}}{3\frac{16}{113} \cdot 4m}}\\\\r_{2}=5,99m
\\\\\\ \small \begin{array}{|l|} \hline h=\\ \hline 4 m \\ \hline 40 dm \\ \hline 400 cm \\ \hline 4\cdot 10^{3} mm \\ \hline 4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline V=\\ \hline 2 m^3 \\ \hline 2\cdot 10^{3} dm^3 \\ \hline 2\cdot 10^{6} cm^3 \\ \hline 2\cdot 10^{9} mm^3 \\ \hline 2\cdot 10^{3} l \\ \hline 20 hl \\ \hline \end{array} \small \begin{array}{|l|} \hline r1=\\ \hline 6 m \\ \hline 60 dm \\ \hline 600 cm \\ \hline 6\cdot 10^{3} mm \\ \hline 6\cdot 10^{6} \mu m \\ \hline \end{array}\\ \small \begin{array}{|l|} \hline r2=\\ \hline 5,99 m \\ \hline 59,9 dm \\ \hline 599 cm \\ \hline 5,99\cdot 10^{3} mm \\ \hline 5,99\cdot 10^{6} \mu m \\ \hline \end{array} \end{array}$