Answer
(a) $4x^3-120x^2+800x$
(b) $0\lt x\lt10$
(c) $1539.6cm^3$
Work Step by Step
(a) The volume V of the box can be expressed as $V=x(40-2x)(20-2x)=4x^3-120x^2+800x$
(b) Let $20-2x>0$ we have $x<10$ and the domain is $x\in (0,10)$
(c) The graph shows that the maximum volume happens when $x=4.23cm, V=1539.6cm^3$
