Practice Maths

Volume Units and Conversion

Key Ideas

Key Terms

cubic millimetre (mm³)
A unit of volume equal to a cube with side length 1 mm.
cubic centimetre (cm³)
A unit of volume equal to a cube with side length 1 cm; 1 cm³ = 1 mL.
cubic metre (m³)
A unit of volume equal to a cube with side length 1 m; 1 m³ = 1 000 000 cm³.
cubic kilometre (km³)
A unit of volume equal to a cube with side length 1 km; used for very large volumes.
capacity
The amount of liquid a container can hold, measured in mL or L.
millilitre (mL)
A unit of liquid capacity; 1 mL = 1 cm³.
litre (L)
A unit of liquid capacity; 1 L = 1000 mL = 1000 cm³.
Volume unit conversions (cube the linear factor):
• 1 cm³ = 1000 mm³   (because 1 cm = 10 mm, so 1 cm³ = 10³ mm³)
• 1 m³ = 1 000 000 cm³   (because 1 m = 100 cm, so 1 m³ = 100³ cm³)
• 1 km³ = 109 m³   (because 1 km = 1000 m, so 1 km³ = 1000³ m³)

Volume–capacity connection:
• 1 cm³ = 1 mL (exact)
• 1 L = 1000 mL = 1000 cm³
• 1 m³ = 1 000 000 cm³ = 1 000 000 mL = 1000 L

Converting volume units

To convert to a smaller unit, multiply by the conversion factor.
To convert to a larger unit, divide by the conversion factor.

Hot Tip For volume conversions, always cube the linear factor. Since 1 m = 100 cm, we get 1 m³ = 100³ cm³ = 1 000 000 cm³. Don’t just multiply by 100 — multiply by 1 000 000! For capacity: 1 cm³ = 1 mL exactly.

Worked Example

Question: Convert 4500 cm³ to litres.

Step 1 — Use the volume–capacity link.
1000 cm³ = 1 L

Step 2 — Divide (going to larger units).
4500 ÷ 1000 = 4.5 L

Volume Units

Volume is measured in cubic units — the amount of space needed to fill a shape with unit cubes. The most common metric volume units are:

  • mm3 (cubic millimetres) — used for very small objects (e.g. a grain of rice, a microchip).
  • cm3 (cubic centimetres) — used for everyday objects (e.g. a juice box, a block of wood). Also written as "cc" in medicine.
  • m3 (cubic metres) — used for large objects (e.g. a room, a shipping container).
  • L (litres) and mL (millilitres) — used for liquids and capacity (how much liquid a container holds).

The key connection: 1 cm3 = 1 mL. A cube with side length 1 cm holds exactly 1 millilitre of liquid. This makes the relationship between volume and capacity very direct: 1000 cm3 = 1 L.

Why Volume Conversions Are Cubes of Length Conversions

This is the most important concept in this lesson. When you convert lengths, you use a single factor: 1 cm = 10 mm, so to convert cm to mm you multiply by 10. But when you convert volumes, you must cube that factor.

Why? Because a 1 cm × 1 cm × 1 cm cube = 1 cm3. Converting to mm: it becomes 10 mm × 10 mm × 10 mm = 1000 mm3. So 1 cm3 = 1000 mm3 (the conversion factor 10 is cubed to get 1000).

Similarly, 1 m = 100 cm, so 1 m3 = 1003 cm3 = 1 000 000 cm3. And 1 m = 1000 mm, so 1 m3 = 10003 mm3 = 1 000 000 000 mm3.

Key Conversion Facts

Memorise these essential conversions:

  • 1 cm3 = 1000 mm3 (103 = 1000)
  • 1 m3 = 1 000 000 cm3 (1003 = 1 000 000)
  • 1 L = 1000 mL
  • 1 L = 1000 cm3
  • 1 mL = 1 cm3
  • 1 m3 = 1000 L (because 1 000 000 cm3 ÷ 1000 = 1000 L)
  • 1 kL (kilolitre) = 1000 L = 1 m3

A handy way to remember: to convert from a larger unit to a smaller unit, multiply. To convert from a smaller unit to a larger unit, divide.

Converting Between Units — Worked Examples

Example 1: Convert 4.5 cm3 to mm3.
1 cm3 = 1000 mm3, so 4.5 cm3 = 4.5 × 1000 = 4500 mm3.

Example 2: Convert 2 500 000 cm3 to m3.
1 m3 = 1 000 000 cm3, so 2 500 000 cm3 = 2 500 000 ÷ 1 000 000 = 2.5 m3.

Example 3: A tank holds 350 L of water. Express this in cm3.
1 L = 1000 cm3, so 350 L = 350 × 1000 = 350 000 cm3.

Example 4: A container has volume 8500 mL. Express in litres.
1 L = 1000 mL, so 8500 mL = 8500 ÷ 1000 = 8.5 L.

Choosing the Right Unit

Always choose a unit appropriate to the context. Using mm3 to describe the volume of a swimming pool would give an unmanageably large number, while using m3 for a tiny medicine capsule gives an unmanageably small number. When answering problems, check which unit gives a sensible answer (not too large, not too small) and convert if needed.

Key tip: Students often forget to cube the conversion factor when converting volume units. A common mistake is converting 5 m3 to cm3 by multiplying by 100 (getting 500 cm3) instead of multiplying by 1003 = 1 000 000 (getting 5 000 000 cm3). Remember: volume is three-dimensional, so the conversion factor must be applied three times — or just remember the cubed result directly: 1 m3 = 1 000 000 cm3.

Mastery Practice

  1. Convert each measurement between mm³ and cm³. Fluency

    1. 5 cm³ = ___ mm³
    2. 8000 mm³ = ___ cm³
    3. 2.5 cm³ = ___ mm³
    4. 3500 mm³ = ___ cm³
    5. 0.4 cm³ = ___ mm³
    6. 750 mm³ = ___ cm³
    7. 12 cm³ = ___ mm³
    8. 6250 mm³ = ___ cm³

  2. Convert each measurement between cm³ and m³. Fluency

    1. 3 m³ = ___ cm³
    2. 2 000 000 cm³ = ___ m³
    3. 0.5 m³ = ___ cm³
    4. 750 000 cm³ = ___ m³
    5. 4.2 m³ = ___ cm³
    6. 3 500 000 cm³ = ___ m³
    7. 0.25 m³ = ___ cm³
    8. 180 000 cm³ = ___ m³

  3. Convert between volume and capacity. Fluency

    1. 250 cm³ = ___ mL
    2. 3000 mL = ___ cm³
    3. 1.5 L = ___ cm³
    4. 4800 cm³ = ___ L
    5. 0.8 m³ = ___ L
    6. 2500 L = ___ m³
    7. 600 cm³ = ___ mL
    8. 7 L = ___ cm³

  4. Perform each mixed volume unit conversion. Understanding

    1. Convert 24 000 mm³ to cm³.
    2. Convert 0.002 m³ to cm³.
    3. Convert 5 L to mm³.
    4. Convert 9 200 000 cm³ to m³.
    5. Convert 350 mL to cm³.
    6. Convert 1.4 m³ to litres.
    7. Convert 48 000 mm³ to mL.
    8. A fish tank holds 180 L. Express this in cm³.
    9. Convert 2 750 000 cm³ to m³.
    10. Convert 0.006 m³ to mL.

  5. Choose the most appropriate unit (mm³, cm³, m³, mL, or L) for each situation. Give a reason. Understanding

    1. The volume of a sugar cube
    2. The capacity of a swimming pool
    3. The volume of a shipping container
    4. The capacity of a medicine dropper (a few drops)
    5. The volume of a grain of rice
    6. The capacity of a kitchen sink
    7. The volume of a refrigerator
    8. The capacity of a water bottle

  6. Solve each problem, showing all working and units at each step. Problem Solving

    1. An aquarium has internal dimensions 80 cm long, 35 cm wide, and 40 cm tall.
      1. Calculate the volume of the aquarium in cm³.
      2. Convert this volume to litres.
      3. Water is added until the tank is 90% full. How many litres of water does the tank contain?
    2. A shipping container has a volume of 33.2 m³.
      1. Convert 33.2 m³ to cm³.
      2. A crate inside the container occupies 12 500 000 cm³. Convert this to m³.
      3. How much space remains in the container (in m³)?
    3. A water tank holds 5000 L when full.
      1. Convert 5000 L to m³.
      2. Convert 5000 L to cm³.
      3. If the tank is currently 40% full, how many litres and how many m³ does it contain?

  7. A swimming pool is a rectangular prism 25 m long, 12 m wide, and 1.5 m deep. Problem Solving

    Tip. Convert all measurements to the same unit before calculating.
    1. Calculate the volume of the pool in m³.
    2. Convert this volume to cm³.
    3. How many litres does the full pool hold?
    4. Water is pumped in at 600 L per minute. How long (in hours and minutes) will it take to fill the pool?

  8. Comparing containers using unit conversions. Problem Solving

    Strategy. Convert all quantities to the same unit before comparing.
    1. Container A has a volume of 2.4 m³ and Container B has a volume of 2 600 000 cm³. Which container is larger? By how many cm³?
    2. A rectangular tank measures 80 cm × 60 cm × 50 cm. It currently holds 168 L of water. What percentage of the tank is full?
    3. A bucket holds 12 L. How many buckets are needed to fill a rectangular trough with dimensions 1.5 m × 0.4 m × 0.5 m?
    4. Convert 3 kL to: (i) L, (ii) cm³, (iii) m³.

  9. Volume, capacity and rate problems. Problem Solving

    Rate problems. Volume ÷ rate = time. Make sure volume and rate use the same units.
    1. A rainwater tank (volume 3 m³) is filled by rain. The roof catchment area is 50 m². How many millimetres of rain are needed to fill the tank? (Hint: 1 mm of rain over 1 m² = 1 L.)
    2. A bathtub holds 250 L. A tap fills it at 15 L per minute. How many seconds does it take to fill?
    3. A storage box measures 60 cm × 40 cm × 30 cm and is filled with liquid that has been measured as 68 400 mL. How full is the box (as a percentage)?
    4. Convert 4.5 kL to mm³. Show all conversion steps.

  10. Investigate volume and capacity in a real-world context. Problem Solving

    Challenge. These problems require multiple conversion steps and careful reasoning about units.
    1. A concrete truck carries 7 m³ of concrete. A path requires concrete to a depth of 10 cm over an area of 60 m². Will one truckload be enough? Show your working.
    2. A fish tank holds 180 L when full. It is rectangular with base dimensions 75 cm × 40 cm. Find the height of the tank in cm.
    3. A region receives 45 mm of rainfall. The region covers 2 km². Calculate the total volume of rain that fell in m³. (Hint: 1 km = 1000 m; convert all to metres.)
    4. A water bottle holds 750 mL. A large cooler holds 15 L. How many full water bottles can be filled from the cooler?
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