[latex]zad.1\ \Dane :\ \d=4sqrt{2} cm , V= 192 cm^3 \ \d=asqrt{2}\ \4sqrt{2}=asqrt{2}/:sqrt{2}\\ a=4 cm\[/latex]
[latex]V=P_{p}*h \ \P_{p}=a^2\ \P_{p}=4^2=16 cm^2 \ \192 = 16 * h/:16\ \h= 12 cm[/latex]
[latex]P_{c}=2P_{p} +P_{b}\ \P_{b}=4a*h\ \P_{b} = 4 * 4 * 12 =192 cm^2 \ \P_{c}=2*16+192 = 32 + 192 =224 cm^2[/latex]
[latex]zad.2)\ \a=8 , alpha =30^o \ \h=frac{asqrt{3}}{2}\ \h=frac{8sqrt{3}}{2}=4sqrt{3}\ \x=frac{1}{3}h\ \x=frac{1}{3} * 4sqrt{3}=frac{4sqrt{3}}{3}[/latex]
[latex]cosalpha =frac{x}{h_{s}}\ \cos30^o=frac{frac{4sqrt{3}}{3}}{h_{s}}\ \cos30^o *h_{s}=frac{4sqrt{3}}{3}\ \frac{sqrt{3}}{2}*h=frac{4sqrt{3}}{3}/*frac{2}{sqrt{3}}\ \h=frac{8}{3}[/latex]
[latex]cosalpha =frac{x}{h_{s}}\ \cos30^o=frac{frac{4sqrt{3}}{3}}{h_{s}}\ \cos30^o *h_{s}=frac{4sqrt{3}}{3}\ \frac{sqrt{3}}{2}*h_{s}=frac{4sqrt{3}}{3}/*frac{2}{sqrt{3}}\ \h_{s}=frac{8}{3}[/latex]
[latex]sinalpha =frac{H}{h_{s}}\ \sin30^o =frac{H}{frac{8}{3}}\ \H=frac{8}{3}*sin30^o\ \H =frac{8}{3}*frac{1}{2}=frac{4}{3}\ \P_{b}=3*frac{1}{2}*a*h_{s}[/latex]
[latex]P_{b}=3*frac{1}{2}*8*frac{8}{3}= 32 [j^2] \ \V=frac{1}{3}P_{p}*H \ \P_{p}=frac{a^{2}sqrt{3}}{4}=frac{8^2sqrt{3}}{4}=frac{64sqrt{3}}{4}=16sqrt{3} [j^2]\ \ V=frac{1}{3}*16sqrt{3}*frac{4}{3}=frac{64sqrt{3}}{9} [j^3][/latex]
[latex]zad.3 \ \a=9 cm \ \promien kuli : R=frac{1}{2} d \ \ przekatna szescinu : d=asqrt{3}\ \d=9 sqrt{3 } cm \ \R= frac{1}{2} *9sqrt{3 }=frac{9sqrt{3}}{2} cm[/latex]
[latex]V=frac{4}{3}pi r^3\ \V=frac{4}{3} pi* (frac{9sqrt{3}}{2})^3=frac{4}{3} pi* frac{81*3sqrt{3}}{8} =frac{81sqrt{3}}{2}pi cm^3[/latex]
