These equations are the resulte from a lagrange multiplier optimization problem. I can not get the algebra right! Please help!
280*pi*r + 80*pi*hi - 2*lamda*r*h = 0
80*pi*r - lamda*pi*r^2=0
-pi*r^2*h + 100=0
Lagrange multiplier problems typically give something like , , etc. I have found that it is often best to divide one equation by another, immediately eliminating (which is not part of the solution, any way).
Here, you have and
Dividing the first equation by the second,
so that .
You can solve that for either r or h in terms of the other and put into the final equation.
(Are you sure about the "hi= pi"? It seems strange that you would write "pi*pi" rather than "pi^2" and also strange that "pi^2" would show up in such a problem.)