Question 978174
If the squares cut from the corners have sides measuring four centimeters,
the height of the box will be {{{4}}} cm.
If the sides of the original square piece of material measured {{{x}}} cm,
the bottom of the box will be a square with sides measuring {{{x-2*4=x-8}}} cm.
{{{drawing(300,300,-1,11,-1,11,rectangle(0,0,10,10),
green(rectangle(2,2,8,8)),locate(4,5.5,green(bottom)),
red(rectangle(0,0,2,2)),red(rectangle(8,8,10,10)),
red(rectangle(0,10,2,8)),red(rectangle(10,0,8,2)),
locate(4.8,-.2,x),arrow(4.7,-0.5,0,-0.5),
arrow(5.3,-0.5,10,-0.5),locate(4,2.6,green(x-2*4)),
locate(1,2,red(4)),locate(9,2,red(4)) )}}}
The surface area of the bottom (in square centimeters) will be {{{(x-8)^2}}} ,
and that, multiplied times the height of the box in cm, {{{(4)}}} ,
is the volume in cubic centimeters:
{{{4(x-8)^2=576}}}
Solving:
{{{4(x-8)^2=576}}}
{{{4(x-8)^2/4=576/4}}}
{{{(x-8)^2=144}}}
{{{x-8=sqrt(144)}}}
{{{x-8=12}}}
{{{x=12+8}}}
{{{x=highlight(20)}}} .
So the box was made from a square piece of material with sides measuring {{{highlight(20cm)}}} .