Question 449938
I think the answer might be to cut 4 x 4 inch squares out of each corner.
If you then fold the sides up, you have a 4 x 4 x 4 box open on top.
the volume is {{{ 4*4*4 = 64 }}} in3
The area is {{{ 5*4*4 = 80 }}} in2
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Call the squares cut out of the corners {{{ x^2 }}}
The surface area is then {{{ A = 144 - 4x^2 }}} in2
The volume is then {{{x* (12 - 2x)^2 }}}
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Suppose I removed  3.99 x 3.99 in2 from each corner
 {{{V = 3.99* (12 - 2*3.99)^2 }}} 
 {{{V = 3.99* (12 - 7.98)^2 }}} 
 {{{V = 3.99* 4.02^2 }}} 
{{{ V = 64.48 }}}
and
{{{ A = 144 - 4*15.92 }}}
{{{ A = 144 - 63.68 }}}
{{{ A = 80.32 }}}
Both volume and area went up.
Now try {{{ x = 4.01 }}}
If either volume goes down or area goes up,
my guess is right