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: 04
$ \text{Gegeben:}\\\text{Mantelfläche} \qquad M\qquad [m^{2}] \\ \text{Mantellinie} \qquad s \qquad [m] \\ \text{Kreiszahl} \qquad \pi \qquad [] \\ \\ \text{Gesucht:} \\ \text{Radius} \qquad r \qquad [m] \\ \\ r = \frac{ M}{s\cdot \pi }\\ \textbf{Gegeben:} \\ M=3\frac{2}{5}m^{2} \qquad s=3\frac{16}{113}m \qquad \pi=120 \qquad \\ \\ \textbf{Rechnung:} \\ r = \frac{ M}{s\cdot \pi } \\ s=3\frac{16}{113}m\\ \pi=120\\ M=3\frac{2}{5}m^{2}\\ r = \frac{ 3\frac{2}{5}m^{2}}{3\frac{16}{113}m\cdot 120 }\\\\r=0,00902m \\\\\\ \small \begin{array}{|l|} \hline M=\\ \hline 3\frac{2}{5} m^2 \\ \hline 340 dm^2 \\ \hline 3,4\cdot 10^{4} cm^2 \\ \hline 3,4\cdot 10^{6} mm^2 \\ \hline 0,034 a \\ \hline 0,00034 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline s=\\ \hline 3\frac{16}{113} m \\ \hline 31,4 dm \\ \hline 314 cm \\ \hline 3,14\cdot 10^{3} mm \\ \hline 3141592\frac{7}{10} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline r=\\ \hline 0,00902 m \\ \hline 0,0902 dm \\ \hline 0,902 cm \\ \hline 9,02 mm \\ \hline 9,02\cdot 10^{3} \mu m \\ \hline \end{array}$