Question 906196
Making a change to your problem description:

<i>A box with a square base and no top is to be made from a square piece of tin by cutting out a 3-inch
Square from each corner and folding up the sides. If the box is hold {{{highlight_green(48)}}} {{{highlight_green(cubic)}}} inches, what size piece of tin should be used?</i>



Let x = length of side of the square piece of tin.


Area of base, {{{(x-2*3)(x-2*3)}}}


Volume of the box, {{{3(x-6)^2=48}}}


Simplify and solve for x.


Divide members by 3,
{{{(x-6)^2=16}}}
{{{x^2-12x+36-16=0}}}
{{{x^2-12+20=0}}}
{{{(x-10)(x-2)=0}}}


The sensible answer will be {{{highlight(x=10)}}}