Question

Pure aluminum metal has density 2.70 g/cm3. If we added a solid aluminum cylinder to a graduated cylinder containing 19.2 mL of water, and the water level rises to 24.7 mL, what is the mass of the aluminum cylinder?

Answer 1

The mass of the aluminum cylinder can be calculated using the density of aluminum (2.70 g/cm3) and the volume of water displaced (5.5 cm3), resulting in a mass of 14.85 grams.

Step-by-step explanation:

To determine the mass of the aluminum cylinder based on a density calculation, one can apply the formula ρ = m/V, where ρ represents density, m stands for mass, and V stands for volume. Given that the density of aluminum is 2.70 g/cm3, we first calculate the volume of the aluminum displaced. The change in water level from 19.2 mL to 24.7 mL indicates a volume displacement of 24.7 mL - 19.2 mL, which equals 5.5 cm3 (since 1 mL = 1 cm3). With this volume and the known density, we can determine the mass of the aluminum, which is given by multiplying the volume displaced (5.5 cm3) by the density of aluminum (2.70 g/cm3):

m = ρ × V = 2.70 g/cm3 × 5.5 cm3 = 14.85 g

Thus, the mass of the aluminum cylinder is 14.85 grams.

Answer 2

According to Archimedes' principle, when an object displaces a liquid in a container, the volume displaced is numerically equal to the volume of the object. So, we solve for the displaced volume, then use the density to determine the mass of the aluminum cylinder.

Volume displaced = Volume of aluminum cylinder = 24.7 mL - 19.2 mL = 5.5 mL

The density is in terms of g/cm³. Note that 1 cm³ is just equal to 1 mL. Therefore,

Mass = 2.70 g/mL * 5.5 mL
Mass = 14.85 g