Question 949300
{{{V=x*x*h=x^2*h}}}
{{{C=2x^2*t+4xh*s}}}
So then,
{{{h=V/x^2}}}
Substituting,
{{{C=2x^2*t+4x(V/x^2)s}}}
{{{C=2tx^2+(4Vs)/x}}}
To minimize C, take the derivative and set it equal to zero.
{{{dC/dx=4tx-(4Vs)/x^2=0}}}
{{{(4Vs)/x^2=4tx}}}

{{{x^3=(Vs)/t}}}
{{{highlight(x=((Vs)/t)^(1/3))}}}
and
{{{h=V/x^2}}}
{{{x^2=((Vs)/t)^(2/3)=V^(2/3)*(s/t)^(2/3)}}}
{{{1/x^2=V^(-2/3)*(t/s)^(2/3)}}}
{{{highlight(h=V^(1/3)*(t/s)^(2/3))}}}