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{Radius} \qquad r \qquad [m] \\ \text{Kreiszahl} \qquad \pi \qquad [] \\ \text{Oberfläche} \qquad O \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Mantellinie} \qquad s \qquad [m] \\ \\ s = \frac{ O}{r\cdot \pi } - r\\ \textbf{Gegeben:} \\ r=3m \qquad \pi=3\frac{16}{113} \qquad O=120m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ s = \frac{ O}{r\cdot \pi } - r \\ r=3m\\ \pi=3\frac{16}{113}\\ O=120m^{2}\\ s = \frac{ 120m^{2}}{3m\cdot 3\frac{16}{113} } - 3m\\\\s=9\frac{52}{71}m \\\\\\ \small \begin{array}{|l|} \hline r=\\ \hline 3 m \\ \hline 30 dm \\ \hline 300 cm \\ \hline 3\cdot 10^{3} mm \\ \hline 3\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline O=\\ \hline 120 m^2 \\ \hline 1,2\cdot 10^{4} dm^2 \\ \hline 1,2\cdot 10^{6} cm^2 \\ \hline 1,2\cdot 10^{8} mm^2 \\ \hline 1\frac{1}{5} a \\ \hline 0,012 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline s=\\ \hline 9\frac{52}{71} m \\ \hline 97,3 dm \\ \hline 973 cm \\ \hline 9,73\cdot 10^{3} mm \\ \hline 9,73\cdot 10^{6} \mu m \\ \hline \end{array}$