Question 1051129
Let the sides of the 4 squares = {{{ x }}}
When the squares are cut out, and sides are
folded up, the sides of the box are:
{{{ x }}} cm
{{{ 10 - 2x }}} cm
{{{ 16 - 2x }}} cm
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The volume is:
{{{ V = x*( 10 - 2x )*( 16 - 2x ) }}}
{{{ V = x*( 160 - 32x - 20x + 4x^2 ) }}}
{{{ V = 4x^3 - 52x^2 + 160x }}}
{{{ V = x^3 - 13x^2 + 40x }}}
Is this for a calculus course?
If so, Set the derivative  = zero
{{{ V[1] = 3x^2 - 26x + 40 }}}
{{{ 3x^2 - 26x + 40 = 0 }}}
Use the quadratic formula
{{{ x = -b +- sqrt( b^2 - 4*a*c )) / ( 2*a ) }}}
{{{ a = 3 }}}
{{{ b = -26 }}}
{{{ c = 40 }}}
Plug in these numbers and find {{{ x }}}
then plug {{{ x }}} back into {{{ V }}} to get
the maximum volume