objetosc walca jest rowna V , a jego pole podstawy P. wyznacz tangens kata nachylenia przekatnej przekroju osiowego walca do plaszczyzny jego podstawy.   odp: [latex]tg alpha=frac{Vsqrt{Ppi}}{2P^2}[/latex] 

[latex]tgalpha = frac{H}{2r}[/latex]     [latex]P=pi r^2[/latex]   [latex]r^2=frac{P}{pi}[/latex]   [latex]r=sqrt{frac{P}{pi}}[/latex]   [latex]V=pi r^2H[/latex]   [latex]H=frac{V}{pi r^2}[/latex]   [latex]H=frac{V}{pi * frac{P}{pi}}[/latex]   [latex]H=frac{V}{P}[/latex]   [latex]tgalpha=frac{frac{V}{P}}{2sqrt{frac{P}{pi}}} * frac{sqrt{frac{P}{pi}}}{sqrt{frac{P}{pi}}} = frac{frac{V}{P}*sqrt{frac{P}{pi}}}{frac{2P}{pi}}= [/latex]   [latex]=frac{V}{P}*frac{pi}{2P}*sqrt{frac{P}{pi}} = frac{V}{P}*sqrt{frac{pi^2}{4P^2}*frac{P}{pi}} =frac{V}{P}*sqrt{frac{pi}{4P}}=frac{V}{P} *sqrt{frac{pi}{4P}*frac{4P}{4P}}=[/latex]   [latex]=frac{V}{P} * frac{sqrt{4Ppi}}{4P}=frac{2Vsqrt{Ppi}}{4P^2}=frac{Vsqrt{Ppi}}{2P^2}[/latex]