Question

Sendo a planificação de um cone um setor circular de raio 6 cm representado na figura acima, calcule o volume do Cone.​

Answer 1

Altura = 3

Raio = 3√3

Volume = (π/3) . Raio² . Altura

Volume = (π/3) . (3√3)² . 3

Volume = (π/3) . 27 . 3

Volume = (π/3) . 81

Volume = 27π

Resposta: 27π cm³

Answer 2

Explicação passo-a-passo:

=> Raio

$\sf \dfrac{2\cdot\pi\cdot g}{2\cdot\pi\cdot r}=\dfrac{360^{\circ}}{\alpha}$

$\sf \dfrac{g}{r}=\dfrac{360^{\circ}}{\alpha}$

$\sf \dfrac{6}{r}=\dfrac{360^{\circ}}{120^{\circ}}$

$\sf 360\cdot r=120\cdot6$

$\sf 360\cdot r=720$

$\sf r=\dfrac{720}{360}$

$\sf \red{r=2~cm}$

=> Altura

Pelo Teorema de Pitágoras:

$\sf r^2+h^2=g^2$

$\sf 2^2+h^2=6^2$

$\sf 4+h^2=36$

$\sf h^2=36-4$

$\sf h^2=32$

$\sf h=\sqrt{32}$

$\sf \red{h=4\sqrt{2}~cm}$

=> Volume

$\sf V=\dfrac{\pi\cdot r^2\cdot h}{3}$

$\sf V=\dfrac{\pi\cdot2^2\cdot4\sqrt{2}}{3}$

$\sf V=\dfrac{\pi\cdot4\cdot4\sqrt{2}}{3}$

$\sf \red{V=\dfrac{16\pi\sqrt{2}}{3}~cm^3}$