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

To determine which box has the greatest density, we need to recall that density is defined as mass per unit volume (density = mass/volume). Since all the boxes have the same volume, we can conclude that the box with the greatest mass will also have the greatest density.

Given the order of the boxes from least to greatest mass:

1. Paper clips (least)
2. Dice
3. Marbles
4. Sand (greatest)

Since sand has the greatest mass, it will also have the greatest density among the four boxes.

Therefore, the answer is: C. the box filled with sand