Question

Considerando que o volume de um cubo de aresta a é a³, observe os cubos abaixo

Answer 1

Explicação passo-a-passo:

A)

V=L²×H

V=x²×x¹

V=x³

B)

$v = ( \frac{2}{3} x) {}^{2} \times \frac{2}{3} x$

$( \frac{2}{3} x) \times ( \frac{2}{3} x) = \frac{4}{9} x {}^{2}$

$v = ( \frac{4}{9} x {}^{2} ) \times ( \frac{2}{3} x)$

$\frac{4}{9} x {}^{2} \times \frac{2}{3}x = \frac{8}{27} x {}^{3}$

Answer 2

$\largea) ~O ~volume ~dos ~cubos \\\\-~ \large V = x^3 \\\\- ~\large V = \dfrac{8}{27} ~x^3$

$\largeb)~ O ~valor ~de~ x \\\\\\\large x = 3$

                              $\large Volume ~de ~s\acute{o}lidos ~geom\acute{e}tricos$

O volume do cubo com a aresta = x

$V = a^3\\\\V = x^3$

O volume do cubo com a aresta = $\dfrac{2}{3} x$

$V = a^3\\\\\\V = (\dfrac{2}{3} x)^3\\\\\\V = (\dfrac{2}{3})^3 ~x^3\\\\\\V = \dfrac{8}{27} ~x^3$

b) Encontrar o valor de x. como a diferença entre os volumes é 19, subtrair os volume e igualar a 19

$x^3 - \dfrac{8}{27} ~x^3 = 19 \\\\\\ \dfrac{ 27x^3 - 8x^3}{27} = 19~. ~27\\\\\\ 27x^3 - 8x^3 = 513\\\\19x^3 = 513\\\\x^3 = \dfrac{513}{19}\\\\x^3 = 27\\\\x = \sqrt[3]{27}\\\\x = 3$

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