Question

A square of a side x inches is cut out of each corner of a 10 in by 18 in piece of cardboard and the sides are folded up form an open topped box

A) write the volume v of the box as a function x
B) find the domain of your function , taking into account restrictions that model imposes in x
C)use your graphing calculator to determine the dimensions of the cut out that will produce the box of maximum volume

Answer 1

dimensions will be \(x, 10-2x, 18-2x\) and so the volume will be
\[V(x)=x(10-2x)(18-2x)\]

Answer 2

as for the domain, if it is a box clearly \(x<0\) and also since one side is only \(10\) you must also have \(10-2x>0\) or \(5>x\)
so a good answer for domain would be \(0<x<5\)

Answer 3

oops i meant "clearly \(x>0\)"

Answer 4

so whats exactly is the domain