PSLE Mathematics Learning Guide · Guide 31
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Capacity and volume problems become unreliable when a learner changes the number but loses the unit, adds litres directly to millilitres, or treats a container’s dimensions as though they were already a liquid amount.
This guide uses one working habit: identify whether the task is measuring container space or liquid amount, choose one compatible unit system, convert before combining quantities, and keep the unit attached through every step.
The MOE Primary Mathematics syllabus updated October 2025 provides curriculum context, while the SEAB 2026 PSLE examination-format page links the current Mathematics syllabus. All examples here are original eduKate teaching material.
Capacity and volume are related but not identical words
Volume measures the three-dimensional space occupied by an object or region. Capacity describes how much a container can hold.
A cuboid tank has an internal volume. That internal space determines its capacity when filled.
In school problems, litres and millilitres are commonly used for liquid capacity, while cubic centimetres and cubic metres are volume units.
Litres and millilitres
1 litre = 1000 millilitres.
2.5 L = 2500 mL.
3750 mL = 3.75 L.
Do not add 2 L + 350 mL as 352 L. Convert or write the mixed unit carefully.
Cubic centimetres and millilitres
In the metric system, 1 cm³ = 1 mL.
A container with internal volume 600 cm³ can hold 600 mL if fully filled, under the idealised mathematical model.
This equivalence is useful when a cuboid’s dimensions are given in centimetres and a liquid answer is requested in millilitres.
Find cuboid volume before converting to capacity
A rectangular tank measures 20 cm × 10 cm × 15 cm internally.
Volume = 20 × 10 × 15 = 3000 cm³.
Capacity = 3000 mL = 3 L.
Guide 7 develops cuboid volume in detail: Rebuild Cube and Cuboid Volume From Base Area and Height.
A partially filled container uses only part of full capacity
A 5 L container is 3/5 full.
Amount of liquid = 3/5 × 5 = 3 L.
Empty space = 2 L.
Do not confuse the amount currently inside with the full capacity.
Pouring problems need state tracking
Jug A contains 1.8 L. Jug B contains 650 mL. If all of B is poured into A:
1.8 L = 1800 mL.
Total = 2450 mL = 2.45 L.
If A has a capacity of only 2.2 L, the mathematical total exceeds capacity by 0.25 L, so overflow must be considered if the problem asks what remains in the container.
Remaining capacity = full capacity − current amount
A tank holds 12 L when full and currently contains 7.35 L.
Remaining capacity = 12 − 7.35 = 4.65 L.
Capacity can combine with rates
A tap fills at 2.5 L/min for 6 minutes.
Amount added = 15 L.
If the tank originally contained 8 L and capacity is 25 L, the theoretical amount would be 23 L, which fits. If the result exceeded 25 L, the capacity ceiling would matter.
Main worked workshop: sixteen original capacity and volume tasks
1.
3.4 L to mL.
Answer: 3400 mL.
2.
4850 mL to L.
Answer: 4.85 L.
3.
2 L + 750 mL.
Answer: 2.75 L.
4.
5.2 L − 850 mL.
Answer: 5200−850=4350 mL=4.35 L.
5.
Volume 750 cm³. Capacity in mL?
Answer: 750 mL.
6.
Cuboid 10×8×5 cm. Capacity?
Answer: 400 cm³ = 400 mL.
7.
Cuboid 25×20×10 cm. Capacity?
Answer: 5000 cm³ = 5 L.
8.
8 L tank is 3/4 full.
Answer: 6 L inside.
9.
Same tank. Empty capacity?
Answer: 2 L.
10.
1.25 L poured into 900 mL.
Answer: 2.15 L total.
11.
Tank capacity 10 L, contains 8.6 L. How much more can fit?
Answer: 1.4 L.
12.
A tap supplies 1.8 L/min for 5 min.
Answer: 9 L.
13.
A 12 L container has 7 L. Add 6 L. How much can remain without overflow?
Answer: 12 L total; 1 L would overflow under the idealised model.
14.
A learner adds 2 L + 300 mL = 302 L.
Repair: 2 L = 2000 mL, so total = 2300 mL = 2.3 L.
15.
A learner says a 4×5×10 cm cuboid holds 200 L.
Repair: volume = 200 cm³ = 200 mL = 0.2 L.
16.
A 6 L container is 40% full.
Answer: 2.4 L inside.
Length, area and volume units are different dimensions
Centimetres measure length. Square centimetres measure area. Cubic centimetres measure volume.
Changing cm to cm³ without a three-dimensional calculation is not a simple unit conversion; it changes the type of quantity.
Common errors
Error 1: Add L and mL without converting.
Error 2: Confuse current liquid amount with full capacity.
Error 3: Treat cubic centimetres as ordinary centimetres.
Error 4: Ignore overflow when a calculated amount exceeds capacity.
Error 5: Convert 1000 mL to 100 L instead of 1 L.
Independent transfer check
- 2.75 L to mL.
- 6250 mL to L.
- 1.6 L + 850 mL.
- Tank 20×12×10 cm: capacity in L.
- 10 L container 65% full: amount inside.
- Explain the relationship between 1 cm³ and 1 mL.
Answers
1. 2750 mL.
2. 6.25 L.
3. 2.45 L.
4. 2400 cm³ = 2.4 L.
5. 6.5 L.
6. In the metric system, one cubic centimetre of volume corresponds to one millilitre of capacity.
Parent and tutor guide
Make the learner label every value with L, mL or cm³ before calculating. For tank questions, separate full capacity, current amount and remaining capacity as three states.
The learner’s final card
Volume or capacity? Which unit is attached? Have I converted before combining? Is the container full, partly full or overflowing? Does the final unit match the requested quantity?
Continue through the PSLE Mathematics Learning Guide
Use Guide 29 and Guide 30. Continue with Guide 32: Measuring Angles.
Return to the PSLE Learning Guide.
Sources and boundaries
Official references: SEAB 2026 PSLE formats and MOE Primary Mathematics syllabus, updated October 2025.
Teaching boundary: All examples and solutions are original eduKate teaching material. The 1 cm³ = 1 mL metric equivalence is stated as a mathematical unit relationship; task-specific syllabus requirements should follow the official materials for the learner’s year.