The volume of a rectangular Chinese box is given by the formula V = LWH. The volume of the box shown on the right is 480 cu units. Find the width and length.

 

The width of the box is ___ units. (Type an integer or a simplified fraction.)

 

An open-top box is to be constructed from a 8 in by 10 in rectangular sheet of tin by cutting out squares of equal size at each corner, then folding up the resulting flaps. Let z denote the length of the side of each cut-out square. Assume negligible thickness. Find a formula for the volume, V, of the box as a function of x. V(x)=_____ For what values of x does the formula from part (a) make sense in the context of the problem? help (inequalities) On a separate piece of paper, sketch a graph of the volume function. What, approximately, is the maximum volume of the box? Give answer to at least 4 decimal places. (include units: help (units))