Volume & Capacity — Grade 5 Mathematics
In Grade 5, we calculate the volume of cuboids using V = l × w × h, understand that 1 cm³ = 1 ml, and solve complex capacity problems involving rates of flow and percentage fill.
Volume of a Cuboid
V = l × w × h
V = 6 × 3 × 4 = 72 cm³
Key equivalence: 1 cm³ = 1 ml 1 000 cm³ = 1 L
So if a box has volume 2 400 cm³, it holds exactly 2 400 ml = 2.4 L.
So if a box has volume 2 400 cm³, it holds exactly 2 400 ml = 2.4 L.
Worked Examples
Example 1 — Calculate Volume
Find the volume of a cuboid 12 cm × 8 cm × 5 cm.
- V = 12 × 8 × 5 = 480 cm³
- This is also 480 ml capacity.
Example 2 — Find a Missing Dimension
A box has volume 360 cm³. Its base is 9 cm × 8 cm. Find the height.
- V = l × w × h → 360 = 9 × 8 × h = 72h
- h = 360 ÷ 72 = 5 cm
Example 3 — Rate of Fill 🚰
A tank (30 cm × 20 cm × 25 cm) fills at 0.5 L per minute. How long to fill it?
- Volume = 30 × 20 × 25 = 15 000 cm³ = 15 L
- Time = 15 L ÷ 0.5 L/min = 30 minutes
Practice Questions
1. Find the volume of a cuboid 7 cm × 5 cm × 4 cm.
✅ 7 × 5 × 4 = 140 cm³
2. Convert 8 500 cm³ to litres.
✅ 8 500 ÷ 1 000 = 8.5 L
3. A cuboid has volume 420 cm³, length 7 cm, width 6 cm. Find the height.
✅ 420 ÷ (7 × 6) = 420 ÷ 42 = 10 cm
4. A container (40 cm × 30 cm × 20 cm) is 75% full. How many litres of liquid is that?
✅ Full volume = 24 000 cm³ = 24 L; 75% of 24 = 18 L
5. Water flows into a tank at 1.2 L per minute. How long to fill a 360 cm³ tank?
✅ 360 cm³ = 0.36 L; 0.36 ÷ 1.2 = 0.3 minutes = 18 seconds
Key Points to Remember
- Volume of cuboid: V = l × w × h, measured in cm³ or m³.
- 1 cm³ = 1 ml; 1 000 cm³ = 1 litre.
- To find a missing dimension: V ÷ (product of known dimensions).
- Capacity is the maximum volume a container can hold.
- Always check units are consistent before multiplying dimensions.