Answer
$5.7\text{ cm}\times 18.6\text{ cm}\times 28.6\text{ cm}$
$V=3032.3\text{ cm}^3$
Work Step by Step
First we write a verbal model of the problem, then write the function in the standard form:
$$\begin{align*}
\text{Volume}=\text{Length}\cdot\text{Width}\cdot\text{Height}.
\end{align*}$$
$$\begin{align*}
V&=(40-2x)\cdot (30-2x)\cdot x\\
&=(1200-140x+4x^2)x\\
&=4x^3-140x^2+1200x.
\end{align*}$$
To find the maximum volume, we graph the volume function using a graphing calculator.
