9.5 Measuring Density
To find a density we need two measurements: the object’s mass and its volume. Mass is easy; volume takes a clever trick when the object has an odd shape.
Measuring mass
Activity 9.3 — Using a balance Mass is the quantity of matter in an object, measured with a balance. On a digital balance: switch it on, place a clean watch glass on the pan, and press tare/reset so it reads zero (this cancels the watch glass’s mass). Now place your object (say, a stone) on it and read off the mass — e.g. 16.4 g.
Mass vs Weight, Again Remember Chapter 5: mass (g, kg) is the amount of matter; weight (N) is the Earth’s pull. Most balances actually measure weight but show it in mass units (g/kg), which works because weight and mass go together on Earth. (Only true two-pan balances compare masses directly.)
Measuring volume
Volume is the space an object occupies (cubic metre, m³; or cm³ and litres for everyday use; 1 mL = 1 cm³). How we measure it depends on the shape.
Liquids and Regular Solids - Liquids: use a measuring cylinder, reading the level at the bottom of the curved surface (the meniscus) with your eye at that level. Choose the right size — a 100 mL cylinder (smallest reading 1 mL) is ideal for 70 mL; too small needs many steps, too large loses accuracy. - Regular solids (cuboids): just measure and multiply, V = l \times w \times h. A 25 cm × 18 cm × 2 cm notebook has a volume of 900 cm³.
Activity 9.7 — Volume by displacement For an irregular object like a stone, use water displacement. Fill a measuring cylinder to, say, 50 mL. Lower the stone in on a thread — the water rises to, say, 55 mL. The object’s volume is the rise:
V = 55\ \text{mL} - 50\ \text{mL} = 5\ \text{mL} = 5\ \text{cm}^3.
Putting it together
Worked Example
A stone has mass 16.4 g and (by displacement) volume 5 cm³. Find its density.
\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{16.4\ \text{g}}{5\ \text{cm}^3} = 3.28\ \text{g/cm}^3.
It’s denser than water, so it would sink.
Did You Know? Earth’s Layers Earth is built in layers of increasing density toward the centre: the crust is lightest, and density rises through the mantle to the core. Deeper down, higher pressure and temperature pack the material into a heavier, more compact state — density at work on a planetary scale.