V=27\pi
\frac{1}{3} \pi r ^2*h=27 \pi /: \pi
\frac{1}{3} r^2 h=27 / *3
r^2h=81
Z trójkata o bokach h r l i 60
\frac{r}{h}=tg60
\frac{r}{h}=\sqrt3
r=\sqrt3h
Podstawiam
(\sqrt3h)^2*h=81
3h^3=81
h^3=27
h=3
Z zależnosci w trójkacie prostok.
mamy l=2h=6
r=3\sqrt3
P_c=\pi r^2+\pi r l=
P_c=\pi* (3\sqrt3)^2+\pi *3\sqrt3*3=
P_c=27\pi +9\sqrt3\pi=9\pi (3+\sqrt3)