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. tap the fields to rank the density values of sample a sample b sample c

Explanation:

Step1: Determine volume of water

The initial volume of water is $V_{water}=100.0\ mL$. Assume the volume - reading intervals on the graduated - cylinder are regular. Let's assume the volume of water + solid for each case:
For sample A, assume the volume reading $V_A = 130\ mL$ (by visual estimation, you may need to refer to the actual scale on the real cylinder). The volume of solid A, $V_{sA}=V_A - V_{water}=130 - 100=30\ mL$. The mass of solid A, $m_A = 578\ g$.
For sample B, assume the volume reading $V_B = 120\ mL$. The volume of solid B, $V_{sB}=V_B - V_{water}=120 - 100 = 20\ mL$. The mass of solid B, $m_B = 545\ g$.
For sample C, assume the volume reading $V_C = 150\ mL$. The volume of solid C, $V_{sC}=V_C - V_{water}=150 - 100 = 50\ mL$. The mass of solid C, $m_C = 722\ g$.

Step2: Calculate density using formula

The density formula is $
ho=\frac{m}{V}$.
For sample A: $
ho_A=\frac{m_A}{V_{sA}}=\frac{578\ g}{30\ mL}\approx19.27\ g/mL$.
For sample B: $
ho_B=\frac{m_B}{V_{sB}}=\frac{545\ g}{20\ mL}=27.25\ g/mL$.
For sample C: $
ho_C=\frac{m_C}{V_{sC}}=\frac{722\ g}{50\ mL}=14.44\ g/mL$.

Step3: Rank the densities

Comparing the values: $
ho_B>
ho_A>
ho_C$.

Answer:

Sample B > Sample A > Sample C