Answer
$2\text{ inches}\times 6\text{ inches}\times 14\text{ inches}$
$V=168\text{ cubic inches}$
Work Step by Step
First we write a verbal model of the problem, then write the function in the standard form:
$$\begin{align*}
\text{Volume}=\text{Length}\cdot\text{Width}\cdot\text{Height}.
\end{align*}$$
$$\begin{align*}
V&=(18-2x)\cdot (10-2x)\cdot x\\
&=(180-56x+4x^2)x\\
&=4x^3-56x^2+180x.
\end{align*}$$
To find the maximum volume, we graph the volume function using a graphing calculator. We will consider only the interval $(0,5)$
