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Year 5 Maths 3D Objects, Volume & Capacity

Choose units for capacity & volume

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Theory

Capacity is how much a container holds: millilitres (mL), litres (L) and kilolitres (kL). Volume is how much space an object takes up: cubic centimetres (\(\text{cm}^3\)) and cubic metres (\(\text{m}^3\)). This Year 5 maths page shows how to choose the right unit, convert between units and compare amounts.

Capacity is the amount a container can hold. Small amounts (a spoon, a cup) are in millilitres; drinks bottles, buckets and baths are in litres; tanks and pools are in kilolitres.

Volume is the space an object takes up. Small objects (a dice, an eraser) are in cubic centimetres (\(\text{cm}^3\)); rooms and shipping containers are in cubic metres (\(\text{m}^3\)).

\(1\text{ L} = 1000\text{ mL}\) and \(1\text{ kL} = 1000\text{ L}\).

A \(1\) cm cube holds exactly \(1\) mL, so \(1\,\text{cm}^3 = 1\text{ mL}\). A \(1\) m cube holds \(1000\) L, so \(1\,\text{m}^3 = 1\text{ kL}\).

Converting kL, L and mL Three boxes kL, L and mL joined by arrows labelled times 1000. Red arrows underneath go back, labelled divide by 1000. kL L mL × 1000 ÷ 1000 × 1000 ÷ 1000
To a smaller unit: \(\times 1000\). To a bigger unit: \(\div 1000\).
Measuring jug A measuring jug marked every 100 mL and labelled every 200 mL up to 1000 mL. The water reaches the 600 mL mark. 2004006008001000mL
The jug holds \(600\) mL of water, which is \(0.6\) L.

Units and how they are linked:

\[ 1\text{ L} = 1000\text{ mL} \]
1 L =1000 mL
\[ 1\text{ kL} = 1000\text{ L} \]
1 kL =1000 L
\[ 1\,\text{cm}^3 = 1\text{ mL} \]
1 cm =1 mL
\[ 1\,\text{m}^3 = 1000\text{ L} = 1\text{ kL} \]
1 m =1000 L =1 kL
Thousand, not hundred. There are 1000 mL in a litre and 1000 L in a kilolitre.
Same unit first. To compare \(1.8\) L and \(1750\) mL, change both to mL.

Converting capacity

  1. Decide whether you are going to a smaller unit (multiply) or a bigger unit (divide).
  2. Multiply or divide by \(1000\).
  3. Check: a smaller unit gives a bigger number.

Choosing a unit

  1. Ask: is it how much it holds (mL, L, kL) or how much space it takes (\(\text{cm}^3\), \(\text{m}^3\))?
  2. Think about size: pick the unit that gives a sensible number.
Example 1 — Choose a unit
Choose the best unit.
(i) A medicine cup
(ii) A kitchen sink
(iii) A town water tank
(iv) A garden shed (volume)
Solution

(i) mL
(ii) L
(iii) kL
(iv) \(\text{m}^3\)

Example 2 — Litres to millilitres
Convert \(6\) L to millilitres.
Solution
\(6 \times 1000\)\(=\)\(6000\text{ mL}\)
6×1000=6000 mL

\(6000\) mL.

Example 3 — Millilitres to litres
Convert \(7500\) mL to litres.
Solution
\(7500 \div 1000\)\(=\)\(7.5\text{ L}\)
7500÷1000=7.5 L

\(7.5\) L.

Example 4 — Decimal litres
Convert \(0.4\) L to millilitres.
Solution
\(0.4 \times 1000\)\(=\)\(400\text{ mL}\)
0.4×1000=400 mL

\(400\) mL.

Example 5 — Cubic units
A tank is \(2\,\text{m}^3\).
(i) How many litres does it hold?
(ii) How many kilolitres?
Solution
\(2 \times 1000\)\(=\)\(2000\text{ L}\)
2×1000=2000 L

(i) \(2000\) L
(ii) \(2\) kL

Example 6 — Compare
Which holds more: a \(1.8\) L bottle or a \(1750\) mL jug?
Solution
\(1.8 \times 1000\)\(=\)\(1800\text{ mL}\)
1.8 L =1800 mL

\(1800\text{ mL} > 1750\text{ mL}\), so the bottle holds more.

Example 7 — Add and subtract
A cooler holds \(8\) L. Sam pours out \(2500\) mL.
(i) How many millilitres are left?
(ii) How many litres is that?
Solution
\(8000 - 2500\)\(=\)\(5500\text{ mL}\)
8000−2500=5500 mL

(i) \(5500\) mL
(ii) \(5.5\) L

Example 8 — Find the mistake
Ivy says a \(600\,\text{cm}^3\) box holds \(6\) L. What is the right answer?
Solution

\(1\,\text{cm}^3 = 1\) mL, so the box holds \(600\) mL, which is \(0.6\) L.

Common pitfalls

Using 100 instead of 1000. \(4200\) mL is \(4.2\) L, not \(42\) L.
Mixing up capacity and volume units. mL, L and kL measure what a container holds; cubic units measure space.
Comparing different units. Change to the same unit before comparing or adding.
Wrong-sized unit. A school hall is about \(2000\,\text{m}^3\), not \(2000\,\text{cm}^3\) (that is only about two litres).

Frequently asked questions

What is the difference between capacity and volume?

Capacity is how much a container holds. Volume is how much space something takes up.

How many millilitres are in a litre?

\(1000\).

How many litres are in a kilolitre?

\(1000\).

How many millilitres fit in one cubic centimetre?

Exactly \(1\) mL.

How many litres fit in a cubic metre?

\(1000\) L, which is \(1\) kL.

Which unit should I use for a swimming pool?

Kilolitres for the water it holds.

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