Four boxes of the same volume are each completely filled with one of the following items:sand, marbles, paperclips, or dice. The order of the boxes from least to greatest mass is as follows: paperclips, dice, marbles, and sand. Which box has the greatest desity?

The answer is sand.

A density (D) is a quotient of mass (m) and volume (V):

D = m/V

The volume is the same, so let it be 1, so we can easily assess the relationship between density and mass:

D = m/1

D = m

So, when mass increases, density increases, too.

Therefore:

paperclips, dice, marbles, sand:

m1 < m2 < m3 < m4

d1 < d2 < d3 < d4