# Homework Help: Liquid Density Puzzle

1. Jul 14, 2009

### Chewy0087

[Solved] Liquid Density Puzzle

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

3. The attempt at a solution

I think there's an assumption here that i'm missing, firstly I worked out how big each cube was by setting up simple simultaneous equations which gave me;

Green = 0.21m Red = 0.14m & Blue = 0.28m

And also Green + Red + Blue = 20kg. From here i'm stuck, I've thought about putting them all together giving me a volume of;

21^3 * 10^-6 + 14^3 * 10^-6 + 28^3 * 10-^6
=9261 +10^-6 + 2744 *10^-6 + 21952 * 10^-6
= 33957 * 10^-6 = 3.3957 * 10^-2 m³

Giving them all a density of 20 / that, but I'm sure it's a dead end =|, can anyone else see a better way of doing this?/An assumption that i'm missing?

Last edited: Jul 14, 2009
2. Jul 14, 2009

### cepheid

Staff Emeritus
From Archimedes' principle, the fact that the cubes are all exactly half-submerged suggests that the glowing liquid is twice as dense as a cube. (Do you understand why?)

3. Jul 14, 2009

### Chewy0087

Hmmm, would that be because half of the volume of the cube of the liquid can support the whole of the cube? :O

However, even given that, how would you work the density of the cube out? Or still do it my way by putting them all together?

Thanks a bunch for the help >.< but i really need to understand this

4. Jul 14, 2009

### cepheid

Staff Emeritus
Yes. This conclusion follows directly from Archimedes' principle, which states that the volume of liquid displaced has a weight that is equal to the weight of the portion of the object submerged.

Considering that you have the total mass and the total volume of the cubes, your method seems good. I can't think of a better way off the top of my head.

5. Jul 14, 2009

### Chewy0087

Thanks again, you rock :P