;
r-радиус основанияж
l- образующая конуса
h-высота
r=4;
\\
l=8;
cos\phi= \frac{r}{l}= \frac{4}{8}= \frac{1}{2} \phi= \frac{\pi}{3}=60^0 " alt="r \geq 0,\ l \geq 0
\\ \left \{ {{\pi rl=\pi32} \atop {r^2+h^2=l^2}} \right.\\
\left \{ {{rl=32} \atop {r^2+48=l^2}} \right. \\
\left \{ {{l=\frac{32}{r} \atop {r^2+48= \frac{32^2}{r^2} }} \right. \\
r^4+48r^2-1024=0;
D=48^2+4096=2304+4096=6400=80^2;\\
r^2= \frac{-48-80}{2}<0;\\
r^2= \frac{-48+80}{2}=16; =>r=4;
\\
l=8;
cos\phi= \frac{r}{l}= \frac{4}{8}= \frac{1}{2} \phi= \frac{\pi}{3}=60^0 " align="absmiddle" class="latex-formula">