A regular block surrenders its volume to a ruler. An odd shaped stone will not, so we let it push water aside instead. The water it displaces is exactly equal to its volume, as long as you account for where the water started.
For a regular solid, calculate the volume from its measured dimensions. For an irregular solid, use displacement: the volume is the rise in level in a measuring cylinder, or the water collected from a Eureka can. In every case, ρ = m / V.
Displacement method: the volume of an irregular solid equals the volume of liquid it displaces.
Then combine with the mass to get the density, ρ = m / V.
Lower the solid into the measuring cylinder and read the level before and after. The volume of the solid is the difference between the two readings, never the final reading alone.
Four quick checks on regular shapes, displacement, and the readings. Each correct answer earns XP and lights this skill on your star map.
The volume of a regular cuboid block is found by...
To find the volume of a small irregular stone, the best method is...
A stone is lowered into a measuring cylinder. The water rises from 50 cm³ to 80 cm³. The volume of the stone is...
When an object is lowered into a full displacement (Eureka) can, the volume of water that overflows equals...
| Regular solid | Irregular solid | |
|---|---|---|
| How to get the volume | measure the dimensions | measure the liquid it displaces |
| Example | V = l × w × h for a block | rise in a measuring cylinder, or a Eureka can |
| Then | find the mass on a balance, and use ρ = m / V | |
A stone of mass 90 g is lowered into a measuring cylinder. The water level rises from 40 cm³ to 70 cm³. Find the density of the stone.
When using a single measuring cylinder, the classic error is dividing the mass by the whole final reading. That includes the water that was already there. The volume of the solid is only the rise in level, the final reading minus the initial reading. Forgetting to subtract the initial volume gives a density that is far too small.
Unlocks once the four checks above are done. Worth more XP, written in the style of Paper 1.
A stone of mass 90 g is lowered into a cylinder and the water rises from 40 cm³ to 70 cm³. The density of the stone is...
Using those readings, a student divides 90 g by 70 cm³ and gets the wrong density. The mistake is that they...
A rectangular block measures 2.0 cm by 3.0 cm by 5.0 cm and has a mass of 120 g. Its density is...
This skill is now lit gold on your star map. That completes the density topic.