The Mass of an Aluminum Cylinder Calculation

Calculation of the Mass of an Aluminum Cylinder

The density (mass/volume) of aluminum is 2.70 x 10³ kilograms per cubic meter (kg/m³). What is the mass of an aluminum cylinder that has a volume of 1.50 m³?

Answer

The answer is 4.05 x 10³ kg.

Step-by-Step Solution

1. Given data:
   • Density (D) of aluminum = 2.70 x 10³ kg/m³
   • Volume (V) of the aluminum cylinder = 1.50 m³
2. Use the formula for density:

   D = m/V

3. Calculate the mass (m):
   • Substitute the known values into the formula:
   • m = D * V
   • Calculate the mass:
   • m = 2.70 x 10³ kg/m³ * 1.50 m³ = 4.05 x 10³ kg

Final answer: The mass of the aluminum cylinder is 4,050 kg, obtained by multiplying the given density of aluminum with the given volume of the cylinder.

Explanation

The mass (m) of the aluminum cylinder can be calculated using the formula for density (ρ), which is Density = Mass/Volume. In this case, since the density of the aluminum (ϱ) is 2.70 x 10³ kilograms per cubic meter (kg/m³) and the volume (V) of the cylinder is 1.50 m³, we can rearrange the formula to find mass such that Mass = Density * Volume. Substituting the given values, we get m = 2.70 x 10³ kg/m³ * 1.50 m³ = 4,050 kg. Therefore, the mass of the aluminum cylinder is 4,050 kg.

The density (D) is a quotient of mass (m) and volume (V) of a substance: D = m/V Step 1. Calculate the volume oWe have: D = 2.70 x 10³ kg/m³ V = 1.50 m³ m = ? D = m/V m = D * V m = 2.70 x 10³ kg/m³ × 1.50 m³ = 4.05 x 10³ kg

The mass of the aluminum cylinder is 4,050 kg, obtained by multiplying the given density of aluminum with the given volume of the cylinder.