Mass, Volume, Weight and Density
Measurements · Mass, Volume, Weight and Density
Syllabus tag: Kenya CBC | Grade 9 Mathematics | Strand 3.0 Measurements | Sub-Strand 3.3 Mass, Volume, Weight and Density (8 Lessons)
Lesson objectives
By the end of this sub-strand, you should be able to:
- Distinguish clearly between mass and weight.
- Determine the density of a substance from its mass and volume.
- Rearrange the density relationship to find any one of the three quantities.
- Apply density to practical problems involving materials, floating and mixtures.
Mass, Volume, Weight and Density
Two boxes can be the same size but not the same to lift. A box of feathers and a box of stones fill the same space and behave very differently.
The idea that explains this is density, and it links three quantities you already measure.
a) Units of mass
Mass tells you how much matter something contains. We measure it in tonnes, kilograms, grams and milligrams.
Every step is a thousand. Going down the list you multiply by 1000. Going up you divide by 1000.
A useful check: the smaller the unit, the bigger the number. Change 5 kg into grams and the answer must be larger than 5. If it is smaller, you went the wrong way.
b) Mass and weight
In everyday speech these two words mean the same thing. In science they do not.
Mass is how much matter is in an object. It never changes. Weight is the pull of gravity on that mass. It changes with where you are.
Mass is measured in kilograms. Weight is measured in newtons.
Your mass on the moon would be exactly the same as in Nairobi. Your weight there would be about one sixth, because the moon pulls more weakly.
c) Density
Density tells you how much mass is packed into each unit of space.
The units follow the rule. Grams divided by cubic centimetres gives g/cm³. Kilograms divided by cubic metres gives kg/m³.
Water has a density of 1 g/cm³. That single number is worth remembering, because it tells you what floats. Anything less dense than water floats. Anything more dense sinks.
d) Working backwards
The same rule finds mass or volume when density is already known. Rearrange it the way you learned in algebra.
To find volume instead, divide the mass by the density.
e) Where this is used
A lorry loading at a quarry must respect an axle load limit, so the driver works in tonnes. Fuel is bought by mass but sold by volume, so a seller has to know its density. A goldsmith checks density to tell real gold from a fake.
Words to know
- Mass -- the quantity of matter in an object, measured in grams, kilograms or tonnes.
- Weight -- the force of gravity acting on a mass, measured in newtons.
- Density -- mass per unit volume, found by dividing mass by volume.
- Tonne -- a unit of mass equal to 1,000 kilograms.
- Relative density -- the density of a substance compared with the density of water.
:::checkpoint Check yourself
- Change 3.2 tonnes into kilograms.
- What is the weight of a 45 kg sack, taking 10 newtons for each kilogram?
- A stone of mass 150 g has a volume of 60 cm³. Find its density.
- Will a material of density 0.7 g/cm³ float or sink in water? :::
Bridge to practice
The exercises begin with direct substitution into the density relationship, move through rearrangement and unit conversion, and finish with two-stage problems where the volume must be calculated first. For every question, write down the units attached to each given value before you start; the questions below are designed so that a units slip produces a plausible-looking wrong option.