[latex]|angle CS_2B|=(180^o-alpha):2=90^o-frac{alpha}{2}[/latex] ------------------ Z trójkąta [latex]CBS_1[/latex] [latex]tgfrac{alpha}{2}=frac{r}{h_1}[/latex] [latex]h_1= frac{r}{tgfrac{alpha}{2}}[/latex] ------------------ Z trójkąta [latex]S_2BS_1[/latex] [latex]tgleft(90^o-frac{alpha}{2} ight) =frac{r}{h_2}[/latex] [latex]ctgfrac{alpha}{2} =frac{r}{h_2}[/latex] [latex]h_2= frac{r}{ctgfrac{alpha}{2}}[/latex] ------------------ Obliczam stosunek objętości [latex]frac{V_1}{V_2}= frac{frac{1}{3}pi r^2h_1}{frac{1}{3}pi r^2h_2}[/latex] [latex]frac{V_1}{V_2}= frac{h_1}{h_2}[/latex] [latex]frac{V_1}{V_2}= frac{frac{r}{tgfrac{alpha}{2}}}{frac{r}{ctgfrac{alpha}{2}}}[/latex] [latex]frac{V_1}{V_2}= frac{frac{1}{tgfrac{alpha}{2}}}{frac{1}{ctgfrac{alpha}{2}}}[/latex] [latex]frac{V_1}{V_2}= frac{ctgfrac{alpha}{2}}{frac{1}{ctgfrac{alpha}{2}}}[/latex] [latex]frac{V_1}{V_2}=ctg^2frac{alpha}{2}}[/latex] [latex]frac{V_1}{V_2}=left(frac{1+cosalpha}{sinalpha} ight)^2[/latex] [latex]frac{V_1}{V_2}=frac{(1+cosalpha)^2}{sin^2alpha}[/latex] [latex]frac{V_1}{V_2}=frac{(1+cosalpha)^2}{1-cos^2alpha}[/latex] [latex]frac{V_1}{V_2}=frac{(1+cosalpha)^2}{(1-cosalpha)(1+cosalpha)}[/latex] [latex]frac{V_1}{V_2}=frac{1+cosalpha}{1-cosalpha}[/latex]
