[tex]\large\text{$1) ~ \cute{A}rea~lareral ~do ~cubo ~ \Rightarrow ~Al = 400 ~cm^2 $}\\\\\large\text{$2) ~ A ~aresta ~do~ cubo ~ \Rightarrow ~a = \sqrt{30} ~cm $}\\\\\large\text{$3) ~O ~Volume ~do ~cubo ~ \Rightarrow ~ V = 1738 ~cm^3$}\\\\\large\text{$4) ~A ~diferen\c{c}a~entre~ as ~\acute{a}reas ~ ~ \Rightarrow ~At ~1050 $}[/tex]
A área lateral do cubo é dada pela formula: [tex]Al = 4.a^2[/tex]
1)
[tex]Al =4.a^2\\\\Al = 4 . ~10^2\\\\Al = 4. ~100\\\\Al = 400 ~cm^2[/tex]
===
2)
[tex]Al = 4 . ~a^2\\\\120 = 4. ~a^2\\\\4a^2 = 120\\\\a^2 = \dfrac{120}{4} \\\\a^2 = 30\\\\a = \sqrt{30} ~cm[/tex]
===
3)
Volume do cubo:
[tex]V = a^3\\\\V = 12^3\\\\V = 1728 ~cm^3[/tex]
===
4)
[tex]At = 6.a^2\\\\At = 6 ~. ~15^2\\\\At = 6 ~. ~225\\\\At = 1350~cm^2[/tex]
[tex]At = 6.a^2\\\\At = 6 ~. ~20^2\\\\At = 6 ~. ~400\\\\At = 2400~cm^2[/tex]
Diferença entre os volumes:
[tex]v2 - v1 \\\\\\2400 - 1350 = > 1050~cm^2[/tex]
===
Para saber mais:
https://brainly.com.br/tarefa/38196708
https://brainly.com.br/tarefa/7707629
https://brainly.com.br/tarefa/6157380
