Question

determine a area total e o volume de um cone reto de geratriz igual a 5cm a altura igual a 4cm

Answer 1

$g=5\ cm\\ h=4\ cm$

Por pitágoras, encontramos o raio da base:

$h^2+r^2=g^2\\\\ 4^2+r^2=5^2\\\\ r^2=25-16\\\\ r^2=9\\\\ \boxed{r=3\ cm}$

Área total:

$A_t=A_b+A_l\\\\ A_t=\pi*r^2+\pi*r*g\\\\ A_t=\pi*3^2+\pi*3*5\\\\ A_t=9\pi+15\pi\\\\ \boxed{A_t=24\pi\ cm^2}$

Volume:

$V=\frac{A_b*h}{3}\\\\ V=\frac{9\pi*4}{3}\\\\ V=\frac{36\pi}{3}\\\\ \boxed{V=12\pi\ cm^3}$