# Thread: The shape of a can

1. ## The shape of a can

1. The problem statement, all variables and given/known data

How do I show that when I have C = 4√(3)r^2 + 2π(r)h + k(4π(r) + h), the cost C to make a cylinder of constant radius V gives the following defining equation: (∛(V))/k = (∛(π(h)/r)) x (2π - h/r)/π(h/r) - 4√(3)

k is the reciprocal of the length that can be joined for the cost of one unit area of metal.

2. Relevant equations

((h/r) = 8/π ≈ 2.55 is the minimized amount of metal used

3. The attempt at a solution

I've tried substituting h = 1000/(πr^2) and then found the derivative with respect to r but it doesn't prove the equation above.
We haven't learn partial derivatives yet, so is there any other way to solve this?

2. Originally Posted by Hydra911
1. The problem statement, all variables and given/known data

How do I show that when I have C = 4√(3)r^2 + 2π(r)h + k(4π(r) + h), the cost C to make a cylinder of constant radius V gives the following defining equation: (∛(V))/k = (∛(π(h)/r)) x (2π - h/r)/π(h/r) - 4√(3)

k is the reciprocal of the length that can be joined for the cost of one unit area of metal.

2. Relevant equations

((h/r) = 8/π ≈ 2.55 is the minimized amount of metal used

3. The attempt at a solution

I've tried substituting h = 1000/(πr^2) and then found the derivative with respect to r but it doesn't prove the equation above.
We haven't learn partial derivatives yet, so is there any other way to solve this?
Post the full question please

CB