A graphing device is recommended. the figure$).$

$($a$)$ Find a function that models the volume $V$ of the box.

$V(x)=$ Well done!

$($b$)$ Find the values of $x$ for which the volume is greater than $240i{n}^3.($Round your answers to three decimal places. Enter your answer using interval notation.$)$

$$

$($c$)$ Find the largest volume $($in $i{n}^3)$ that such a box can have. $($Round your answer to three decimal places.$)$

$i{n}^3$