Question

a graduated cylinder is filled with 100.0 ml of water. the cylinder is placed on a mass balance and tared (zeroed). in three different studies, samples of solid are added to the cylinder. the mass of solid and the new volume reading are shown.

Explanation:

Step1: Recall density formula

The density formula is $
ho=\frac{m}{V}$, where $
ho$ is density, $m$ is mass and $V$ is volume. The initial volume of water is $V_0 = 100.0\ mL$. Let's assume the volume - reading after adding the solid is $V_1$. The volume of the solid $V=V_1 - 100.0\ mL$. But since we are ranking and the initial volume of water is the same for all, we can just compare $\frac{m}{V_1}$ (as the subtraction of 100 from $V_1$ for each case will not change the ranking).

Step2: Analyze the mass - volume relationship for ranking

For Sample A, $m_A = 722\ g$. For Sample B, $m_B = 578\ g$. For Sample C, $m_C = 343\ g$. Without knowing the exact volume readings, if we assume the volume increases in a linear - like fashion with the addition of mass (and since the initial volume is the same), the sample with the largest mass will have the highest density if the volume increase is not disproportionately large. Since $m_A>m_B>m_C$, we can rank the densities as follows.

Answer:

Sample A > Sample B > Sample C