Question

A metalworker wants to make an open box from a sheet of metal, by cutting equal squares from each corner as shown. The maximum volume is approximately ___ in.^3 and is generated when x=___ in. (Round to one decimal place as needed.) Length=24-2xWidth=12-2xHeight=x

Answer 1

a) The dimensions of the open box are

Length = 24 - 2x

Width = 12 - 2x

Height = x

b) Recall that the volume of a rectangular prism is given by

`V=l\cdot w\cdot h`

So, the function for the volume of the open box becomes

`V=(24-2x)\cdot(12-2x)\cdot x`

c) Let us have a look at the graph of the above function

Notice that the maximum volume of the open box is approximately 332.6 in³

This maximum volume occurs when x is equal to 2.5 in

x = 2.5 in