Question

A manufacturer makes closed cubic containers from sheet metal. How many square centimeters of sheet metal will a 27,000 cm 3 container need?

Answer 1

let's recall that a cube is just a rectangular prism with all equal sides, check picture below.

`\bf \textit{volume of a cube}\\\\ V=s^3~~ \begin{cases} s=&length~of\\ &a~side\\ \cline{1-2} V=&27000 \end{cases}\implies 27000=s^3\implies \sqrt[3]{27000}=s\implies 30=s \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a cube}\\\\ SA=6s~~\begin{cases} s=&length~of\\ &a~side\\ \cline{1-2} s=&30 \end{cases}\implies SA=6(30)\implies SA=180`