Question

Um cone reto possui geratriz igual a 5 cm e altura de 3 cm. Determine as medias da area total e o volume desse cone.​

Answer 1

$\large- A ~ \acute{a}rea ~ total ~do ~cone ~ \Rightarrow ~ At = 113,04 ~cm^2\\\\\large- Volume ~do ~cone~ \Rightarrow ~ V=50,24 ~cm^3$

Encontrar o valor do raio do cone:

Usar a formula de Pitágoras para encontrar o valor do raio.

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

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$\pi = 3,14\\g = 5 ~cm\\r = 4 ~cm$

Área total do cone:

$At = \pi ~.~r~. ~ (g+r)\\\\At = 3.14 ~.~4~. ~ (5+4)\\\\At = 12,56~. ~ (9)\\\\At = 12,56~. ~ (9)\\\\At = 113,04 ~cm^2$

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Volume do cone:

$V = \dfrac{1}{3} ~\pi~. ~r^2~. ~h\\\\\\V = \dfrac{1}{3} ~3.14~. ~4^2~. ~3\\\\\\V = \dfrac{1}{3} ~3.14~. ~16~. ~3\\\\\\V = \dfrac{1}{3} ~3.14~. ~48\\\\\\V = \dfrac{1}{3} ~150,72\\\\\\V = \dfrac{150,72}{3} \\\\\\V=50,24 ~cm^3$

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