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Question
An aluminium block has a volumeThe volume of a three-dimensional shape is a measure of the amount of space or capacity it occupies, eg an average can of fizzy drink has a volume of 330 cm3. of 480 cm3. What is the massThe amount of matter an object contains. Mass is measured in kilograms (kg) or grams (g). of the block if the densityThe density of a material is the mass of 1 cm3 (or 1 m3) of the material. It is a measure of the compactness of a material. Density is measured in grams per centimetre cubed (g/cm3) or kilograms per metre cubed (kg/m3). of aluminium is 2.7 g/cm3?
\(m=vx\rho\)
\(\rho=2.7 g/cm^3\)
\(v=480 cm^3\)
m = 480 cm3 x 2.7 g/cm3
m = 1296 g
The mass of the aluminium block is 1 296 g or 1.296 kg.
The units of density
For small volumes density is measured in g/cm3.
For larger volumes density is measured in kg/m3.
- To convert from kg/m3 to g/cm3, divide by 1000.
- To convert from g/cm3 to kg/m3, multiply by 1000.
Aluminium has a density of 2.7 g/cm3 = 2,700 kg/m3.
Water has a density of 1.0 g/cm3, or 1000 kg/m3.
Knowing the density of a material enables an engineer or architect to calculate the mass of a building or structure from its volume.
This in turn enables them to determine the correct depth of foundation to make the building safe.
Question
An Olympic size swimming pool measures 50 m long, 25 m wide and has an average depth 2 m. What is the mass of water in the pool if the density of water is 1000 kg/m3?
The swimming pool is a regular shape and so the volume of water is calculated using the equation:
Volume = length x breadth x height
Volume = 50 m x 25 m x 2 m = 2500 m3
m = \(v \times \rho\)
\(\rho = \)1000 kg/m3
v = 2500 m3
m = 2500 m3 x 1000 kg/m3
m = 2,500,000 kg
The mass of water in the swimming pool is 2,500,000 kg or 2500 tonnes.