Question

Um cone reto tem altura 8cm e raio da base 6cm. Determine A)a área de sua baseB)sua área lateralC)sua área totalD)seu volume.

Answer 1

$\large a) ~A~ \acute{a}rea ~da ~base ~ \Rightarrow ~Ab = 36 ~\pi ~cm^2\\\\\large b) ~A~ \acute{a}rea ~da ~lateral ~ \Rightarrow ~Al = 60 ~\pi ~cm^2 \\\\\large c) ~A ~ \acute{a}rea ~da ~total ~ \Rightarrow ~ At = 96 ~\pi ~cm^2 \\\\\large d) ~O~ Volume ~ \Rightarrow ~ 96~\pi ~cm^3$

a) A área de sua base:

$Ab = r^2 ~. ~\pi\\\\Ab = 6^2 ~. ~\pi\\\\Ab = 36 ~\pi ~cm^2$

b) A área lateral:

Encontrar a geratriz do cone:

$g^2 = h^2 + r^2\\\\g^2 = 8^2 + 6^2\\\\g^2 = 64 + 36\\\\g^2 = 100\\\\g = \sqrt{100}\\\\g = 10 ~cm$

$Al = \pi ~. ~r~.~g\\\\Al = \pi ~. ~6~ .~ 10\\\\Al = 60 ~\pi ~cm^2$

c) A área total:

$At = \pi ~.~r ~. ~(g+r)\\\\At = \pi ~.~6 ~. ~(10+6)\\\\At = \pi ~.~6 ~. ~(16)\\\\At = 96 ~\pi ~cm^2$

d) volume:

$V = \dfrac{1}{3} ~\pi~. ~r^2~. ~h\\\\\\V = \dfrac{1}{3} ~\pi~. ~6^2~. ~8\\\\\\V = \dfrac{1}{3} ~\pi~. ~36~. ~8\\\\\\V = \dfrac{1}{3} ~\pi~. ~288\\\\\\V = \dfrac{288}{3} ~\pi\\\\\\V = 96~\pi ~cm^3$

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