Geometrie-Stereometrie-Kreiszylinder

$V = r^{2} \cdot \pi \cdot h$
1 2
$r = \sqrt{\frac{ V}{\pi \cdot h}}$
1
$h = \frac{ V}{r^{2} \cdot \pi }$
1
$O = 2\cdot r\cdot \pi \cdot (r+h)$
1 2
$r = 0,5\cdot (-h+\sqrt{h^{2} +\frac{O}{\pi }})$
1
$h = \frac{0-2\cdot \pi \cdot r^{2} }{ 2\cdot r\cdot \pi }$
1
Beispiel Nr: 02
$\begin{array}{l} \text{Gegeben:}\\\text{Körperhöhe} \qquad h \qquad [m] \\ \text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Radius} \qquad r \qquad [m] \\ \\ \text{Gesucht:} \\\text{Volumen} \qquad V \qquad [m^{3}] \\ \\ V = r^{2} \cdot \pi \cdot h\\ \textbf{Gegeben:} \\ h=5m \qquad \pi=3\frac{16}{113} \qquad r=10m \qquad \\ \\ \textbf{Rechnung:} \\ V = r^{2} \cdot \pi \cdot h \\ h=5m\\ \pi=3\frac{16}{113}\\ r=10m\\ V = (10m)^{2} \cdot 3\frac{16}{113} \cdot 5m\\\\V=1,57\cdot 10^{3}m^{3} \\\\\\ \small \begin{array}{|l|} \hline h=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline r=\\ \hline 10 m \\ \hline 100 dm \\ \hline 10^{3} cm \\ \hline 10^{4} mm \\ \hline 10^{7} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline V=\\ \hline 1,57\cdot 10^{3} m^3 \\ \hline 1570796\frac{7}{20} dm^3 \\ \hline 1,57\cdot 10^{9} cm^3 \\ \hline 1,57\cdot 10^{12} mm^3 \\ \hline 1570796\frac{7}{20} l \\ \hline 1,57\cdot 10^{4} hl \\ \hline \end{array} \end{array}$