WeBWorK using host: https://webwork-ptx.aimath.org, format: simple seed: 139

An open-top box is to be constructed from a by rectangular
sheet of tin by cutting out squares of equal size at each corner,
then folding up the resulting flaps.
Let denote the length of the side of each cut-out square. Assume negligible thickness.

(a) Find a formula for the volume, , of the box as a function of .

(b) For what values of does the formula from part (a) make sense
in the context of the problem? help (inequalities)

(c) On a separate piece of paper, sketch a graph of the volume function.

(d) What, approximately, is the maximum volume of the box? (include units: help (units))