Question

Um cone circular reto tem 3 cm de raio e 15 pi cm² de area lateral. Qual é o seu volume?

Answer 1

Área lateral

$A_l=\pi*r*g\\\\ 15\pi=\pi*3*g\\\\ 3g=15\\\\ g=\frac{15}{3}\\\\ \boxed{g=5\ cm}$

Volume

$V=\frac{A_b*h}{3}\\\\ h^2+r^2=g^2\\\\ h^2+3^2=5^2\\\\ h^2=25-9\\\\ h^2=16\\\\ \boxed{h=4\ cm}\\\\ V=\frac{\pi*3^2*4}{3}\\\\ V=\frac{36\pi}{3}\\\\ \boxed{V=12\pi\ cm^3}$