Homework Help: Surface Area help

1. Apr 14, 2012

JuliusDarius

1. The problem statement, all variables and given/known data
Imagine you have a rectangular piece of cardboard measuring 3 feet by 4 feet. You know that if you cut a square out of each corner, you can fold the pieces together and tape them together to make an object that looks like a shoe box:http://www.omahamathtutor.com/wp-content/uploads/2012/03/shoebox.png
What is the outside surface area of this shoe box shape that maximize the volume?

2. Relevant equations
2ab + 2bc + 2ac

3. The attempt at a solution
Not sure where to start

2. Apr 14, 2012

Bohrok

V = L*W*H

Then express the length, width, and height in terms of x after you remove those four squares from the 4 x [STRIKE]12[/STRIKE] 3 rectangle.

Last edited: Apr 14, 2012
3. Apr 14, 2012

JuliusDarius

Could you show me how to do that?

4. Apr 14, 2012

Bohrok

The length is originally 4, then you cut off two segments of length x from both ends of that side, so L = 4 - 2x. Same thing for the width.

After cutting out the four squares, you have four flaps that fold up; what would be the height of these flaps?