# Need to find the volume of a 3d object

1. Aug 11, 2010

### 619snake

I'm here again bothering you, I have this problem, but have no idea about how to start the problem solving:
1. The problem statement, all variables and given/known data
The USPS will accept packages only if the length plus girth is no more than 108 inches.
Assuming that the front face is square, what is the largest volume package that the USPS will accept?

I have attached a picture of the package that is shown on the problem.

I know that I have not attempted to do this problem, but as I explained, I just want to know how to start it, because the professor never explained a similar problem, he just did it with area and the volume of a box that needed to have some squares cut to use it as an open box

some formulas I know I need are:

g(girth) = 2(W + H)

V = L x W x H

that's all I know

plz help =(

#### Attached Files:

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2. Aug 11, 2010

### Sina

You have to write the defining equations as (assume you have the maximum length 108):

L + G = 108 => 2(W+H) + L =108

Now the real valued function you want to maximize is f(L,W,H) = L*W*H subject to the constraint 2(W+H) + L -108 =0. In this case you an you Lagrange multiplier method that is gradient(f) = a.gradient(constraint). Then this yields (WH, LH, LW) = a.(1, 2,2). From here you find WH = a, LH=2a, LW=2a => H/W = 2 and W/L = 1/2. From here you can find the solution.

3. Aug 11, 2010

### Staff: Mentor

The goal here is to find the largest value of V, subject to the constraint that the length + girth is <= 108 ".

Given that the face of the box is a square, V = W2 * L. Use the constraint to write the volume as a function of a single variable. Then do what you would normally do to find the maximum value.

4. Aug 11, 2010

### 619snake

Thanks people, solved the problem