# Finding min. value of dimensions for a tank of water

1. Nov 27, 2013

### BOAS

Hello

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

An open tank is constructed with a square base and vertical sides to hold 32m3 of water. Find dimensions of the tank if the area of the sheet metal used to make it is to have a minimum value.

2. Relevant equations

3. The attempt at a solution

I'm not entirely sure of how to approach this problem beyond needing to use the second derivative. I think I need to construct an expression of the area related to volume.

So,

the sides pf the base, x multiply together to give an area x2 and the four sides can be called 4xh (side of the base multiplied by height)

x2 + 4xh is an area of sheet metal

x2h = 32

I don't know how to proceed.

2. Nov 27, 2013

### Staff: Mentor

The only thing you're missing is that your volume function can be solved for h as a function of x, and then substituted into your surface area function, making it a function of x alone. Once you have the surface area as a function of x, use the usual technique for finding the minimum value.

3. Nov 27, 2013

### BOAS

ah of course! Thanks

4. Nov 27, 2013

### Ray Vickson

Besides the hint already given, you can also use the Lagrange multiplier method (if you know about it).

5. Nov 28, 2013