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: 01
$ \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=7m \qquad \pi=8 \qquad r=4m \qquad \\ \\ \textbf{Rechnung:} \\ V = \frac{1}{3}\cdot r^{2} \cdot \pi \cdot h \\ h=7m\\ \pi=8\\ r=4m\\ V = \frac{1}{3}\cdot (4m)^{2} \cdot 8 \cdot 7m\\\\V=298\frac{2}{3}m^{3} \\\\\\ \small \begin{array}{|l|} \hline h=\\ \hline 7 m \\ \hline 70 dm \\ \hline 700 cm \\ \hline 7\cdot 10^{3} mm \\ \hline 7\cdot 10^{6} \mu m \\ \hline \end{array} \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 V=\\ \hline 298\frac{2}{3} m^3 \\ \hline 298666\frac{2}{3} dm^3 \\ \hline 298666666\frac{2}{3} cm^3 \\ \hline 2,99\cdot 10^{11} mm^3 \\ \hline 298666\frac{2}{3} l \\ \hline 2986\frac{2}{3} hl \\ \hline \end{array}$