4solid cubes were made out of the same material. each of the four side cubes have different side lengths which are: 6cm, 8cm, 10cm, and 12cm. your task is to divide the cubes onto two sides of a scale so that the two sides are even. which cube (or cubes) do you put on one side, and subsequently which remaining cube (or cubes) do you put on the other side?

Since all cubes are made of the same material, they have the same density. This means that equal pieces taken from each of the cubes will have the same mass, and therefore weight. This means that all we need to know is volume- how big the cubes are.

Volume is three dimensional, so we need to use units cubed. This is helpful since with actual cubes, you can just multiply the side length by itself three times.

The volumes are:

Again, because the densities are the same we only need the volume. If they weren't we would have to calculate the mass.

The final step is just to figure out how to balence the equation, and therefore the scale. The volume on side A needs to equal the volume on side B. Here, the volumes of the three smallest cubes equals the volume of the largest.

216+512+1000=1728

The reason the differences between the cubes gets bigger each time, despite adding exactly 2 cm, is that the values are cubed. The difference between x and y is much smaller than the difference between x^n and y^n.