Hi...I'm working on a problem for the minimization of materials for a can. This juice can should hold 163 mL, and I'm already stuck on the first step. When setting up the minimization equation I should be able to graph it and get an idea of about where the minimum should be. I've got 2*Pi*r^2 + 326/r so far, but the graph doesn't show anything that looks like a zero slope anywhere - it just looks like a standard sqrt function. So before I go further with this, what am I doing wrong?
If we cut this same can from hexagons instead, thereby saving even more material, could I write the area as a function of the radius as such: A(r) = 6*(1/2)(2/r)(r)? because 1/2 b*h = A; b = 2/r and the height = radius. Problem with this is that my variable cancel themselves out and I'm not sure what to do with that. Do I need to be using trig formulas?
x = (1/r*sin90)/(sin(45)) = sin(45)/r = (sqrt(2))/2r.