Is the crown real gold?
Over 2,000 years ago, King Hiero of Syracuse gave a goldsmith a bar of gold to turn into a crown. The crown came back weighing exactly as much as the bar. Then a rumour: the goldsmith kept some gold and mixed in cheaper silver. The story goes that Archimedes was asked to find out, without scratching or melting the crown. You get his tools, plus a digital scale.
Grade 8 science · FluidsMass, volume, densityAbout 12 min
Part 1 of 4 · The case
Weigh it, then dunk it
Weighing alone can't catch the goldsmith: the crown has the same mass as the gold bar. So measure the other thing, how much space it takes up. Dunk it in a full overflow can, and the water it pushes out spills into a measuring cylinder. That's its volume.
Try: pick the gold bar, put it on the scale, then dunk it.
Notebook
| Object | Mass | Volume | Mass ÷ volume |
|---|
1 mL of water pushed out = 1 cm³ of object.
Before you dunk the crown: it weighs the same as the gold bar. Will it push out…
Your verdict
Line up the three numbers on a density ruler. Where does the crown land?
Part 2 of 4 · Cut it, plot it
Does a smaller piece have less density?
Lots of people think cutting something in half halves its density. Saw some blocks and put every piece on a mass–volume graph. Mass goes up the side, volume along the bottom.
Try: pick a block, plot it, then saw it in half and plot again. Do it a few times.
Four mystery samples
Every piece of one material lands on one straight line through zero. The steepness of that line is the density. So you can name a material from one dot. The dashed lines are reference metals.
Try: tap a sample to plot it, then name it.
Quick one: a 5 kg pine plank or an 8 g gold ring. Which is denser?
Part 3 of 4 · Inside the stuff
Same particles, different spacing
Take 18 g of water: the same particles every time. Freeze it, melt it, boil it. The particles don't change size and none go missing. What changes is how far apart they sit.
Try: drag the temperature from −20 °C to 120 °C and watch the volume.
Part 4 of 4 · Stack it
Build a density tower
Six kitchen liquids, one tall glass. Pour them in any order you like, even the "wrong" one.
Try: pour all six. Then predict where each object stops, and drop it in.
Liquids
Objects
Tap an object, then tap the layer it will float on (or the bottom button).
Putting it back together
What density is, and isn't
- Density = mass ÷ volumeHow many grams are packed into each cubic centimetre. Gold packs 19.3, water 1, air about 0.0012.
- A material, not an objectSaw it, grow it, shrink it: every piece of gold sits on the same line. Heavy and dense are different questions.
- Spacing, not sizeSolid, liquid and gas have the same particles; gas particles are just far apart. Water is odd: its solid is less dense, so ice floats and lakes freeze from the top.
- Denser goes downLiquids stack by density, not by pouring order, and an object stops on the first layer denser than itself.
And the crown? Its density came out between gold and silver: the goldsmith had swapped about 30% of the gold. Next: why the same egg sinks in tap water and floats in salt water.