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{Mantellinie} \qquad s \qquad [m] \\ \text{Radius} \qquad r \qquad [m] \\ \text{Kreiszahl} \qquad \pi \qquad [] \\ \\ \text{Gesucht:} \\\text{Oberfläche} \qquad O \qquad [m^{2}] \\ \\ O = r\cdot \pi \cdot (r+s)\\ \textbf{Gegeben:} \\ s=4m \qquad r=6m \qquad \pi=3\frac{16}{113} \qquad \\ \\ \textbf{Rechnung:} \\ O = r\cdot \pi \cdot (r+s) \\ s=4m\\ r=6m\\ \pi=3\frac{16}{113}\\ O = 6m\cdot 3\frac{16}{113} \cdot (6m+4m)\\\\O=188m^{2} \\\\\\ \small \begin{array}{|l|} \hline s=\\ \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 r=\\ \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 O=\\ \hline 188 m^2 \\ \hline 1,88\cdot 10^{4} dm^2 \\ \hline 1884955\frac{31}{50} cm^2 \\ \hline 1,88\cdot 10^{8} mm^2 \\ \hline 1\frac{100}{113} a \\ \hline 0,0188 ha \\ \hline \end{array}$