# Archimede's Principle Problem

1. Oct 29, 2006

### Menisto

A closed cubical box made of aluminum sheet floats in water with (1/4) of the volume above water. Determine the thickness of the sheet.

I first found out what the density would need to be for this orientation:

75% below water or

X % = density of box/ density of water

.75 = p/(1000)

p = 750 kg/m^3 --> effective density.

p = M(sheet) / Volume(box)

Mass of the sheet is then = 6p(s^2)x

where s is the length of a side of the cube, x is the thickness of the sheet and p is the density of aluminum (2700 kg/m^3)

M = 16200 x(s^2)

Therefore: 750 = 16200 x(s^2) / s^3

.0463 = x/s

The problem is, there seems to be not enough information.

2. Oct 29, 2006

### Menisto

Am I correct in assuming this?

3. Oct 29, 2006

### OlderDan

You are correct. Surface area is not proportional to volume. Even if you did a more precise calculation of the volume of aluminum as the difference between outer volume and inner volume, you can still go from essentially a solid cube of aluminum to a huge cube with a very small ratio of aluminum volume to air volume (low density) using the same thickness of walls. There has to be more information to solve the problem.

4. Oct 29, 2006

### Menisto

Ok, thank you. I thought I was going crazy there for a second, too many hours of homework. It doens't help when the professor makes his own course packet, and has to correct problems and answers for every homework set. It gets a little frustrating.