When a 5.00-g metal piece, A, was immersed in 38.0 mL of water, the water level rose to 50.0 mL. Similarly, when a 5.00-g metal piece, B, was immersed in 38.0 mL of water, the level of water rose to 60.0 mL. Compare the density of the metal pieces. A and B. Show your work.

In this case, we first need to take into account that the density of each metal A and B is computed by dividing the mass over the volume of each metal which is actually computed by substracting the volume of water from the volume of the water and the solid:

[tex]V_A=50.0mL-38.0mL=12.0mL\\\\V_B=60.0mL-38.0mL=22.0mL[/tex]

Next, we compute the densities as shown below:

[tex]\rho_A=\frac{m_A}{V_A}=\frac{5.00g}{12.0mL}=0.42g/mL\\ \\\rho_B=\frac{m_B}{V_B}=\frac{5.00g}{22.0mL}=0.23g/mL[/tex]

In such a way, A is denser is B as it's volume for the same mass is smaller.

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