Mass, Volume and Density
Section: Physics | Syllabus: Cambridge Lower Secondary Checkpoint Science (0893)
Mass and Volume
- Mass is the amount of matter in an object, measured in grams (g) or kilograms (kg)
- Volume is the amount of space an object occupies, measured in cm³ or m³
- Mass and volume are different properties – an object can have a large volume but small mass, or vice versa
- a large polystyrene container – takes up lots of space (large volume) but is light (small mass)
- a small bag of nails – takes up little space (small volume) but is heavy (large mass)
- Important terms:
- Hollow: contains air or empty space inside (e.g., football, balloon, empty bottle)
- Solid: no air spaces inside – completely filled with matter (e.g., metal block, rock, marble)
Calculating Volume
Regular Shapes
For objects with regular shapes (cuboids, cubes), we can calculate volume using a formula – this is the simplest method for finding volume.
- Formula: Volume = Length × Width × Height
- Units: mm³, cm³, or m³
Worked Example: Wooden Block
Museli measures a wooden block with a length of 10 cm, a width of 5 cm and a height of 2 cm, and wants to find its volume.
- Step 1: write down the formula. Volume = Length × Width × Height
- Step 2: substitute the values. Volume = 10 cm × 5 cm × 2 cm
- Step 3: calculate the answer. Volume = 100 cm³
Irregular Shapes
For objects with irregular shapes (rocks, stones, ornaments), we cannot use a simple formula. Instead, we use the displacement method – a technique to find the volume of an irregular object by measuring how much water it displaces (pushes aside) when submerged.
The displacement method: the rise in water level equals the volume of the submerged object
- Step-by-step method:
- fill a measuring cylinder with water and record the initial volume (e.g., 50 cm³)
- carefully lower the irregular object into the water (make sure it's fully submerged)
- record the new volume reading (e.g., 75 cm³)
- calculate: Volume of object = New volume – Initial volume
Worked Example: Rock Volume
Muumbe places a rock in a measuring cylinder containing 50 cm³ of water, and the water level rises to 75 cm³.
- Step 1: write down the formula. Volume of rock = New volume – Initial volume
- Step 2: substitute the values. Volume of rock = 75 cm³ – 50 cm³
- Step 3: calculate the answer. Volume of rock = 25 cm³
Understanding Density
Density tells us how much mass is packed into a certain volume. It explains why some objects feel heavy for their size while others feel light.
- Density is the mass per unit volume of a substance, measured in g/cm³ or kg/m³
- Formula: Density = Mass ÷ Volume
The Density Formula Triangle
Cover the quantity you want to find, and the triangle shows how to calculate it from the other two
- To find Density: cover D → Density = Mass ÷ Volume
- To find Mass: cover M → Mass = Density × Volume
- To find Volume: cover V → Volume = Mass ÷ Density
Converting Between g/cm³ and kg/m³
Density can be given in g/cm³ or in kg/m³. Some exam questions give densities in kg/m³, so you need to be able to work with (and compare) both units.
- To convert g/cm³ → kg/m³: multiply by 1000
- To convert kg/m³ → g/cm³: divide by 1000
- Water's density: 1.0 g/cm³ = 1000 kg/m³
Worked Example: Comparing Densities Given in kg/m³
Mia investigates floating and sinking in water, which has a density of 1000 kg/m³. She wants to work out whether an object of density 400 kg/m³ and an object of density 2700 kg/m³ will float or sink.
- Step 1: keep all the densities in the same unit (kg/m³) so they can be compared directly - here, everything is already given in kg/m³, so no conversion is needed
- Step 2: compare each object's density with water's density of 1000 kg/m³
- Step 3: 400 kg/m³ is less than 1000 kg/m³, so this object floats; 2700 kg/m³ is greater than 1000 kg/m³, so this object sinks
Worked Example: Iron and Polystyrene Blocks
Muchindu has an iron block with a mass of 790 g and a volume of 100 cm³, and a polystyrene block with a mass of 5 g and the same volume, and wants to compare their densities.
- Step 1: write down the formula. Density = Mass ÷ Volume
- Step 2: substitute the iron block's values. Density = 790 g ÷ 100 cm³ = 7.9 g/cm³
- Step 3: substitute the polystyrene block's values. Density = 5 g ÷ 100 cm³ = 0.05 g/cm³
- Step 4: compare. The iron is much more dense than the polystyrene – it has much more mass packed into the same volume
Calculating Density
- Step-by-step method:
- identify the mass (in g or kg)
- identify the volume (in cm³ or m³)
- write the formula: Density = Mass ÷ Volume
- substitute the values
- calculate and include the correct units
Worked Example: Aluminium
Museli has a piece of aluminium with a mass of 270 g and a volume of 100 cm³, and wants to find its density.
- Step 1: write down the formula. Density = Mass ÷ Volume
- Step 2: substitute the values. Density = 270 g ÷ 100 cm³
- Step 3: calculate the answer. Density = 2.7 g/cm³
Worked Example: Wood (Two-Step Problem)
Muumbe has a wooden block with a mass of 48 g and dimensions of 4 cm × 4 cm × 3 cm, and wants to find its density.
- Step 1: calculate the volume. Volume = 4 cm × 4 cm × 3 cm = 48 cm³
- Step 2: write down the density formula. Density = Mass ÷ Volume
- Step 3: substitute the values. Density = 48 g ÷ 48 cm³
- Step 4: calculate the answer. Density = 1.0 g/cm³
Comparing Densities
Different materials have different densities. Here's a comparison of common materials:
| Material | Density (g/cm³) | State |
|---|---|---|
| Helium | 0.00018 | Gas |
| Air | 0.0013 | Gas |
| Wood (pine) | 0.5 | Solid |
| Water | 1.0 | Liquid |
| Concrete | 2.4 | Solid |
| Aluminium | 2.7 | Solid |
| Iron | 7.9 | Solid |
| Lead | 11.3 | Solid |
| Gold | 19.3 | Solid |
| Osmium | 22.6 | Solid |
Interactive revision notes, videos and practice questions load below.