Convert square and cubic units of length
Key Notes:
📏 Understanding Units of Length
- Length units measure how long something is.
- Common units 👉 mm, cm, m, km
🟦 Square Units (Area) – When measuring surfaces
Square units are used to measure area (2D shapes like floor, land, walls).
✨ Examples:
- mm² (square millimetre)
- cm² (square centimetre)
- m² (square metre)
- km² (square kilometre)
📣 Remember:
When converting square units, you multiply or divide by the square of the conversion factor.
| Conversion | Multiply / Divide | 💡 Rule |
|---|---|---|
| cm² → m² | ÷ 10,000 | because 1m=100cm and 100² = 10,000 |
| m² → cm² | × 10,000 | reverse conversion |
| m² → km² | ÷ 1,000,000 | 1000²=1,000,000 |
| km² → m² | × 1,000,000 | reverse conversion |
📍 Example:
Convert 500 cm² to m²
→ 500÷10,000=0.05m²
🧊 Cubic Units (Volume) – When measuring space
Cubic units measure volume (3D objects like boxes, tanks, rooms).
✨ Examples:
- mm³ (cubic millimetre)
- cm³ (cubic centimetre)
- m³ (cubic metre)
- km³ (cubic kilometre)
📣 Remember:
When converting cubic units, multiply or divide by the cube of the conversion factor.
| Conversion | Multiply / Divide | 💡 Rule |
|---|---|---|
| cm³ → m³ | ÷ 1,000,000 | because 1m=100cm and 100³=1,000,000 |
| m³ → cm³ | × 1,000,000 | reverse conversion |
| m³ → km³ | ÷ 1,000,000,000 | 1000³=1,000,000,000 |
| km³ → m³ | × 1,000,000,000 | reverse |
📍 Example:
Convert 3,000 cm³ to m³
→ 3000÷1,000,000=0.003m³
🔢 Quick Tricks to Remember
| Type | Multiply/Divide by |
|---|---|
| Length | 10, 100, 1000 |
| Area (Square) | 10²=100,100² = 10,0001000² =1,000,000 |
| Volume (Cubic) | 10³ = 1,00100³=1,000,000,1000³ =1,000,000,000 |
🧠 Tip:
- Square → 2 zeros
- Cubic → 3 zeros
(When converting between cm ↔ m)
✅ Why Do We Use Square and Cubic Units?
| Unit Type | Used For | Example |
|---|---|---|
| Square (2D) | Area | Classroom floor, land |
| Cubic (3D) | Volume | Water tank, fridge, room |
🏆 Practice to Master
- Convert between units step-by-step
- Always write the conversion factor
- Check if your answer is smaller or bigger than original
Learn with an example
Convert:
1,000 cubic millimetres = ——— cubic centimetres
Start with the given quantity, 1,000 cubic millimetres:
1,000 mm3
Next, write a conversion factor to convert millimetres to centimetres. Make sure the conversion factor has millimetres in the denominator so that the units cancel properly. Since the units are cubed, multiply by the conversion factor three times.
1,000 cubic millimetres = 1 cubic centimetre
Convert:
——- square metres = 1,000,000 square millimetres
Start with the given quantity, 1,000,000 square millimetres:
1,000,000 mm2
Next, write a conversion factor to convert millimetres to metres. Make sure the conversion factor has millimetres in the denominator so that the units cancel properly. Since the units are squared, multiply by the conversion factor twice.
Convert:
1 cubic centimetre = ——– cubic millimetres.
Start with the given quantity, 1 cubic centimetre:
1 cm3
Next, write a conversion factor to convert centimetres to millimetres. Make sure the conversion factor has centimetres in the denominator so that the units cancel properly. Since the units are cubed, multiply by the conversion factor three times.
1 cubic centimetre = 1,000 cubic millimetres
let’s practice!
