Problema se reduce la determinarea unor elemente ale conului.
[tex]\it h_{con}=h_{cilindru}\\ \\ \mathcal{A}_{\ell. con}=\mathcal{A}_{\ell. cilindru} \Rightarrow \pi RG=2\pi Rh\bigg|_{:\pi R} \Rightarrow G=2h\\ \\ \\ \Delta O'OB\ -\ dreptunghic,\ \widehat O=90^o,\ \stackrel{T.P.}{\Longrightarrow}\ 4h^2-h^2=25\cdot3\bigg|_{:3} \Rightarrow\\ \\ \\ \Rightarrow 3h^2=25\cdot3 \Rightarrow h^2=25 \Rightarrow h=5\ cm;\ \ \ G=2h=2\cdot5=10\ cm\\ \\ \\ \mathcal{A}_{\ell. con}=\pi RG=\pi\cdot5\sqrt3\cdot10=50\sqrt3\pi\ cm^2[/tex]
[tex]\it \mathcal{V}_{con}=\dfrac{\pi R^2 h}{3}=\dfrac{\pi\cdot25\cdot3\cdot5}{3}=125\pi\ cm^3[/tex]
