Answer:
140608 cubic in
Step-by-step explanation:
[tex]x+x+h=156[/tex]
[tex]h=156-2 x[/tex]
[tex]V=x^{2} h \quad[/tex] We eliminate one of the variables
[tex]V=x^{2}(156-2 x)[/tex]
[tex]V=156 x^{2}-2 x^{3}[/tex] Differentiating [tex]v[/tex]
[tex]V^{\prime}=312x-6 x^{2} \quad[tex] When [/tex]V=0[/tex]
[tex]312x-6 x^{2}=0[/tex]
[tex]x(312-6 x)=0 \quad=\quad\left\{\begin{array}{l}x=0 \\ x=52 \quad x=0 \text { not acceptable }\end{array}\right.[/tex]
[tex]h=156-2(52)=\Rightarrow h=52[/tex]
[tex]V=52\times52\times52= 140608 \text{ cubic in}[/tex]
