Question

A cylindrical can has radius r and height h. The amount of steel in the can is proportional to the surface area A = 2(pi)r(h+r) of the can. For a fixed volume V of the can, nd the critical points of the area A. Using your answer find the dimensions
of the cylindrical can which use the least steel (for a fixed volume).

Answer 1

solve A in terms of either r or h, your choice.
then take the first derivative ( assuming you are in calc) and find the max
if your not in calc
still solve in terms of r or h (still your choice)
then find the vertexof the parabila

Answer 2

ok thank you

Answer 3

actually I found the right way of doing it, MCronin answer is not correct

Answer 4

please explain

Answer 5

we need to use f(r,h) = A and find critical points on a path c=V=(pi)r^2h where V is constant, I think its the right way of doing it will try to solve it and give the answer

Answer 6

thats one way to do it i dont use partial derivatives unless i have to though and you will have to use them using f(r,h)=A

Answer 7

I get my dimensions as r=(v/(2(pi))^1/3 and h = ((4V)/pi)^1/3

Answer 8

that is correct, i also get those dimensions