Grade 10 Math · Litres and cubes
The litre is secretly a cube
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The litre is secretly a cube

Good news: the litre is a cube in disguise. One litre is exactly a 10 cm × 10 cm × 10 cm cube — the milk-carton cube — so 1 L=1000 cm31\ \mathrm{L} = 1000\ \mathrm{cm}^3. Work a volume in cm³, slide the decimal three places, and you're speaking litres. Going up a size, one cubic METRE holds a thousand of those litre cubes: 1 m3=1000 L1\ \mathrm{m}^3 = 1000\ \mathrm{L} — a full hot tub, a tonne of water.

Now the trap this lesson exists for: lengths convert by 100, but VOLUMES convert by 100 cubed. A metre holds 100 centimetres, so a metre cube holds 100×100×100=1,000,000100 \times 100 \times 100 = 1{,}000{,}000 centimetre cubes — a million, not a hundred. Convert the lengths first, or cube the bridge — never let a flat ×100 anywhere near a volume.