Question

Um cilindro equilátero tem 1000 cm³ de volume. Determine sua altura

Answer 1

Explicação passo-a-passo:

Em um cilindro equilátero, temos $\sf h=2r$

Temos que:

$\sf V=\pi\cdot r^2\cdot h$

$\sf V=\pi\cdot r^2\cdot2r$

$\sf V=2\cdot\pi\cdot r^3$

$\sf 1000=2\cdot\pi\cdot r^3$

$\sf r^3=\dfrac{1000}{2\pi}$

$\sf r=\sqrt[3]{\dfrac{1000}{2\pi}}$

$\sf r=\dfrac{10}{\sqrt[3]{2\pi}}$

$\sf r=\dfrac{10}{\sqrt[3]{2\pi}}\cdot\dfrac{\sqrt[3]{4\pi^2}}{\sqrt[3]{4\pi^2}}$

$\sf r=\dfrac{10\sqrt[3]{4\pi^2}}{2\pi}$

$\sf r=\dfrac{5\sqrt[3]{4\pi^2}}{\pi}~cm$

Logo:

$\sf h=2\cdot\dfrac{5\sqrt[3]{4\pi^2}}{\pi}~cm$

$\sf h=\dfrac{10\sqrt[3]{4\pi^2}}{\pi}~cm$

$\sf \red{h\approx10,84~cm}$