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{Kreiszahl} \qquad \pi \qquad [] \\ \text{Volumen} \qquad V \qquad [m^{3}] \\ \text{Radius} \qquad r \qquad [m] \\ \\ \text{Gesucht:} \\\text{Höhe} \qquad h \qquad [m] \\ \\ h = \frac{3\cdot V}{r^{2} \cdot \pi }\\ \textbf{Gegeben:} \\ \pi=3\frac{16}{113} \qquad V=4m^{3} \qquad r=7m \qquad \\ \\ \textbf{Rechnung:} \\ h = \frac{3\cdot V}{r^{2} \cdot \pi } \\ \pi=3\frac{16}{113}\\ V=4m^{3}\\ r=7m\\ h = \frac{3\cdot 4m^{3}}{(7m)^{2} \cdot 3\frac{16}{113} }\\\\h=0,078m \\\\ \small \begin{array}{|l|} \hline V=\\ \hline 4 m^3 \\ \hline 4\cdot 10^{3} dm^3 \\ \hline 4\cdot 10^{6} cm^3 \\ \hline 4\cdot 10^{9} mm^3 \\ \hline 4\cdot 10^{3} l \\ \hline 40 hl \\ \hline \end{array} \small \begin{array}{|l|} \hline r=\\ \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 h=\\ \hline 0,078 m \\ \hline 0,78 dm \\ \hline 7,8 cm \\ \hline 78 mm \\ \hline 7,8\cdot 10^{4} \mu m \\ \hline \end{array}$