Question

Qual o volume de um cone onde a geratriz mede 5 cm e o diâmetro 6 cm?

Answer 1

$\largeO ~Volume ~do ~cone ~ \Rightarrow ~ V = 12 ~\pi ~cm^3$

                                    $\largeS\acute{o}lidos ~Geom\acute{e}tricos$

Encontrar o valor do raio da base do cone:

$r = \dfrac{di\hate{a}metro}{2}\\\\\\r = \dfrac{6}{2}\\\\\\r = 3 ~cm$

Com o valor do raio e a geratriz do cone encontrar a altura ( h) do cone.

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

Volume do cone:

$V = \dfrac{1}{3} ~\pi~. ~r^2~. ~h\\\\\\V = \dfrac{1}{3} ~\pi~. ~3^2~. ~4\\\\\\V = \dfrac{1}{3} ~\pi~. ~9~. ~4\\\\\\V = \dfrac{1}{3} ~\pi~. ~36\\\\\\V = \dfrac{36}{3} ~\pi\\\\\\V = 12 ~\pi ~cm^3$

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