A full can of black cherry soda has a mass of 0.406 kg. It contains 3.38 10-4 m3 of liquid. Assuming that the soda has the same density as water, find the volume of aluminum used to make the can.

To find the volume of aluminum used to make the can, we need to subtract the volume of the liquid from the total volume of the can.

Given:
Mass of the can (m) = 0.406 kg
Density of water (ρ) = Density of soda (ρ) [since we assume soda has the same density as water] = 1000 kg/m^3
Volume of liquid (V) = 3.38 x 10^-4 m^3

First, let's calculate the mass of the liquid using the density and volume:
Mass of liquid (ml) = Density x Volume of liquid
ml = ρ x V
ml = 1000 kg/m^3 x 3.38 x 10^-4 m^3
ml = 0.338 kg

Now, let's calculate the mass of the aluminum used to make the can:
Mass of aluminum (ma) = Total mass - Mass of liquid
ma = m - ml
ma = 0.406 kg - 0.338 kg
ma = 0.068 kg

Next, we'll calculate the density of aluminum (ρa), which is typically around 2700 kg/m^3.

Now, using the equation Density = Mass/Volume, we can find the volume of aluminum used:
Volume of aluminum (Va) = Mass of aluminum / Density of aluminum
Va = ma / ρa
Va = 0.068 kg / 2700 kg/m^3
Va ≈ 2.518 x 10^-5 m^3

Therefore, the volume of aluminum used to make the can is approximately 2.518 x 10^-5 m^3.