Calculation of Aluminum Density

In this section, we will calculate the density of aluminum using the given weight measurements of a block of aluminum in air and water.

First, we will need to find the mass of aluminum. The mass of aluminum can be calculated by finding the difference between its weight in air and water. The weight of the aluminum block in air was 450 kg while in water it was 284 kg. Therefore, the mass of aluminum can be calculated as follows:

Mass of aluminum = Weight in air - Weight in water

Mass of aluminum = 450 kg - 284 kg

Mass of aluminum = 166 kg

Next, we will use the Archimedes' principle to calculate the volume of aluminum. According to the principle, the buoyant force acting on a submerged object is equal to the weight of the displaced fluid. We know that the weight of water displaced by the aluminum block is equal to the weight of the block in air minus the weight of the block in water. The density of water is 1000 kg/m^3. Therefore, the volume of aluminum can be calculated as follows:

Volume of aluminum = (Weight in air - Weight in water) / Density of water

Volume of aluminum = (450 kg - 284 kg) / 1000 kg/m^3

Volume of aluminum = 0.166 m^3

Finally, we can calculate the density of aluminum by dividing the mass of aluminum by its volume. Therefore, the density of aluminum can be calculated as follows:

Density of aluminum = Mass of aluminum / Volume of aluminum

Density of aluminum = 166 kg / 0.166 m^3

Density of aluminum = 1000 kg/m^3

Therefore, the density of aluminum is 1000 kg/m^3.

In conclusion, we have successfully calculated the density of aluminum using the given weight measurements and Archimedes' principle.