Geometrie-Stereometrie-Kreiskegel

• $V = \frac{1}{3}\cdot r^{2} \cdot \pi \cdot h$
1 2
$r = \sqrt{\frac{3\cdot V}{\pi \cdot h}}$
1
$h = \frac{3\cdot V}{r^{2} \cdot \pi }$
1
$O = r\cdot \pi \cdot (r+s)$
1
$s = \frac{ O}{r\cdot \pi } - r$
1 2 3
$r = \frac{-\pi \cdot s + \sqrt{(\pi \cdot s)^{2} +4\cdot \pi \cdot O}}{ 2\cdot \pi }$
1 2 3
$M = r\cdot \pi \cdot s$
$s = \frac{ M}{r\cdot \pi }$
1 2 3 4
$r = \frac{ M}{s\cdot \pi }$
1 2 3 4 5
$s =\sqrt{h^{2} + r^{2} }$
1
$r =\sqrt{s^{2} - h^{2} }$
1
$h =\sqrt{s^{2} - r^{2} }$
1

Beispiel Nr: 02
$\text{Gegeben:}\\\text{Höhe} \qquad h \qquad [m] \\ \text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Radius} \qquad r \qquad [m] \\ \\ \text{Gesucht:} \\\text{Volumen} \qquad V \qquad [m^{3}] \\ \\ V = \frac{1}{3}\cdot r^{2} \cdot \pi \cdot h\\ \textbf{Gegeben:} \\ h=5m \qquad \pi=1 \qquad r=2m \qquad \\ \\ \textbf{Rechnung:} \\ V = \frac{1}{3}\cdot r^{2} \cdot \pi \cdot h \\ h=5m\\ \pi=1\\ r=2m\\ V = \frac{1}{3}\cdot (2m)^{2} \cdot 1 \cdot 5m\\\\V=6\frac{2}{3}m^{3} \\\\\\ \small \begin{array}{|l|} \hline h=\\ \hline 5 m \\ \hline 50 dm \\ \hline 500 cm \\ \hline 5\cdot 10^{3} mm \\ \hline 5\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline r=\\ \hline 2 m \\ \hline 20 dm \\ \hline 200 cm \\ \hline 2\cdot 10^{3} mm \\ \hline 2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline V=\\ \hline 6\frac{2}{3} m^3 \\ \hline 6666\frac{2}{3} dm^3 \\ \hline 6666666\frac{2}{3} cm^3 \\ \hline 6,67\cdot 10^{9} mm^3 \\ \hline 6666\frac{2}{3} l \\ \hline 66\frac{2}{3} hl \\ \hline \end{array}$