diff options
| -rw-r--r-- | Mathe/10/5/Aufgaben/Oberflaecheninhalt_Rot_Trichter.tex | 9 |
1 files changed, 5 insertions, 4 deletions
diff --git a/Mathe/10/5/Aufgaben/Oberflaecheninhalt_Rot_Trichter.tex b/Mathe/10/5/Aufgaben/Oberflaecheninhalt_Rot_Trichter.tex index b0ab443f..58e46081 100644 --- a/Mathe/10/5/Aufgaben/Oberflaecheninhalt_Rot_Trichter.tex +++ b/Mathe/10/5/Aufgaben/Oberflaecheninhalt_Rot_Trichter.tex @@ -29,13 +29,14 @@ $r_k = f = 1$ \\ \end{tabular} \vspace{5mm} \noindent{}Gesucht: \\ -$O = (G_K - G_{HK}) + (M_K - M_k) + O_{HK}$ \BE{2} \\ +$O = (G_K - G_{HK}) + (M_K - M_k) + O_{HK} + G_k$ \BE{2} \\ $(G_K - G_{HK}) = 2\pi \cdot (g+h)^2 - 2\pi \cdot h^2 = 32\pi cm^2$ \BE{1} \\ $O_{HK} = 2 \pi \cdot r^2 = 2\pi\cdot r_{HK} = 18\pi cm^2$ \BE{1} \\ %$h_K = \sqrt{k^2 - r_K^2} = \sqrt{7^2 - 5^2} = \sqrt{24}$ \BE{1} $\frac{r_K}{r_k} = \frac{m_K}{m_k} \Rightarrow m_k = m_K \cdot \frac{r_k}{r_K} = \frac{7}{5}cm$ \BE{1} \\ % $h_k = \sqrt{m_k^2 - f^2} = \sqrt{\frac{24}{25}}$ \BE{1} \\ -$M_K = \pi \cdot r_K \cdot k = 35\pi cm^2$ \\ -$M_k = \pi \cdot r_k \cdot m_k = \frac{7}{5}\pi cm^2$ \BE{1} \\ -$O = 32\pi cm^2 + (35\pi cm^2 - \frac{7}{5}\pi cm^2) + 18\pi cm^2 = 72,6\pi cm^2 \approx \SI{228}{cm^2}$ \BE{1} +$M_K = \pi \cdot r_K \cdot k = 35\pi cm^2$ \BE{0.5} \\ +$M_k = \pi \cdot r_k \cdot m_k = \frac{7}{5}\pi cm^2$ \BE{0.5} \\ +$G_k = \pi \cdot r_k^2 = \pi \cdot 1cm^2 = \pi cmd^2$ \BE{1} \\ +$O = 32\pi cm^2 + (35\pi cm^2 - \frac{7}{5}\pi cm^2) + 18\pi cm^2 + \pi cm^2= 73,6\pi cm^2 \approx \SI{231}{cm^2}$ \BE{1} \end{Lsg} |