# The shape of a can

• Dec 10th 2010, 01:12 AM
Hydra911
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?
• Dec 10th 2010, 04:59 AM
CaptainBlack
Quote:

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?