Question

Ilustrati desfasurarea unui con circular drept cu generatoarea de 6 cm si raza bazei de 2,5cm.Calculati aria laterala,aria totala si volumul acestui con.
Va rog frumos )))

Answer 1

$G=6 \ cm \\ r=2,5 \ cm \\ A_l=\pi \cdot r \cdot G \\ A_l=2,5 \ cm \cdot 6 \ cm\cdot \pi \\ \Rightarrow \boxed{A_l=15\pi \ cm^2} \\ A_t=A_l+A_b \\ A_b=\pi \cdot r^2 \\ A_b=\pi \cdot (2,5)^2 \ cm^2 \\ A_b=6,25 \pi\ cm^2 \\ A_t=15\pi \ cm^2+6,25 \pi \ cm^2 \\ \boxed{A_t=21,25\pi \ cm^2}\\ V= \frac{r^2 \cdot h \cdot \pi}{3} \\ G^2=h^2+r^2 \\ h^2=G^2-r^2 \\ h^2=6^2 \ cm^2-(2,5)^2 \ cm^2 \\ h^2=36 \ cm^2-6,25 \ cm^2 \\ h^2=29,75 \ cm^2 \\ h=\sqrt{29,75 } \ cm$
$V= \frac{(2,5)^2 \ cm^2 \cdot \sqrt{29,75} \cdot \pi }{3}\\ \Rightarrow \boxed{V= \frac{6,25\sqrt{29,75} \pi}{3} \ cm^3}$