Question

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. which box has the greatest density?
a. the box filled with paper - clips
b. the box filled with sand
c. the box filled with dice
d. the box filled with marbles

Explanation:

Step1: Recall density formula

Density $
ho=\frac{m}{V}$, where $m$ is mass and $V$ is volume.

Step2: Analyze given volumes and masses

Volumes of boxes are equal ($V_{1}=V_{2}=V_{3}=V_{4}$). Mass order is paper - clips < dice < marbles < sand.

Step3: Determine density based on formula

Since $
ho=\frac{m}{V}$ and $V$ is constant, density is directly proportional to mass. So the box with the greatest mass has the greatest density. Sand has the greatest mass among the items, so the box filled with sand has the greatest density.

Answer:

B. the box filled with sand