$ \text{Gegeben:}\\\text{Oberfläche} \qquad O \qquad [m^{2}] \\ \text{Mantellinie} \qquad s \qquad [m] \\ \text{Kreiszahl} \qquad \pi \qquad [] \\ \\ \text{Gesucht:} \\ \text{Radius} \qquad r \qquad [m] \\ \\ r = \frac{-\pi \cdot s + \sqrt{(\pi \cdot s)^{2} +4\cdot \pi \cdot O}}{ 2\cdot \pi }\\ \textbf{Gegeben:} \\ O=3m^{2} \qquad s=3\frac{16}{113}m \qquad \pi=120 \qquad \\ \\ \textbf{Rechnung:} \\ r = \frac{-\pi \cdot s + \sqrt{(\pi \cdot s)^{2} +4\cdot \pi \cdot O}}{ 2\cdot \pi } \\ O=3m^{2}\\ s=3\frac{16}{113}m\\ \pi=120\\ r = \frac{-120 \cdot 3\frac{16}{113}m + \sqrt{(\pi \cdot s)^{2} +4\cdot \pi \cdot 3m^{2}}}{ 2\cdot \pi }\\\\r=0,00794m \\\\\\ \small \begin{array}{|l|} \hline O=\\ \hline 3 m^2 \\ \hline 300 dm^2 \\ \hline 3\cdot 10^{4} cm^2 \\ \hline 3\cdot 10^{6} mm^2 \\ \hline \frac{3}{100} a \\ \hline 0,0003 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 0,00794 m \\ \hline 0,0794 dm \\ \hline 0,794 cm \\ \hline 7,94 mm \\ \hline 7,94\cdot 10^{3} \mu m \\ \hline \end{array}$