Grade 5 Mathematics Measurement – Volume Notes
Mathematics — Measurement
Subtopic: Volume (Age 10 — Kenyan context)
Volume is the amount of space inside an object. For liquids we call it capacity. Examples: how much water a jerrycan holds or how much maize fits in a box.
- Millilitre (mL) — small amounts (e.g., a medicine spoon: 5 mL).
- Litre (L) — common for water and milk (e.g., a 2 L soda bottle).
- Cubic centimetre (cm³) — used for small solid volumes (1 cm³ = 1 mL).
- Cubic metre (m³) — for large tanks or rooms (used rarely at this level).
Quick conversions:
1 L = 1000 mL
1 mL = 1 cm³
1 L = 1000 cm³
1 m³ = 1000 L
1 mL = 1 cm³
1 L = 1000 cm³
1 m³ = 1000 L
- Cuboid (rectangular box): Volume = length × width × height.
- Cube (all sides equal): Volume = side × side × side = side³.
Use the formula:
Cuboid: V = l × w × h (units: cm³ or m³ or L if for liquid capacity)
Cube: V = side³
Cube: V = side³
Example 1 — Cuboid
A shoe box has length 30 cm, width 20 cm and height 12 cm. Find its volume.
Solution: V = l × w × h = 30 × 20 × 12 = 30 × 240 = 7200 cm³.
Since 1 cm³ = 1 mL, the box holds 7200 mL = 7.2 L (if filled with water).
A shoe box has length 30 cm, width 20 cm and height 12 cm. Find its volume.
Solution: V = l × w × h = 30 × 20 × 12 = 30 × 240 = 7200 cm³.
Since 1 cm³ = 1 mL, the box holds 7200 mL = 7.2 L (if filled with water).
Example 2 — Cube
A cube block has side 5 cm. Find its volume.
Solution: V = side³ = 5 × 5 × 5 = 125 cm³ = 125 mL.
A cube block has side 5 cm. Find its volume.
Solution: V = side³ = 5 × 5 × 5 = 125 cm³ = 125 mL.
Example 3 — Capacity conversion (Kenyan context)
A small jerrycan holds 20 L of water. How many mL is this?
20 L = 20 × 1000 mL = 20,000 mL.
A small jerrycan holds 20 L of water. How many mL is this?
20 L = 20 × 1000 mL = 20,000 mL.
- Use a measuring jug for liquids (read at eye level).
- For boxes, measure length, width and height in the same unit (cm or m).
- Convert to litres if you talk about water jerrycans or bottles.
- Remember: 1 cm³ = 1 mL — handy for small containers.
- Find the volume of a rectangular tank 150 cm long, 80 cm wide and 60 cm deep. Give answer in litres.
- A cube has volume 216 cm³. What is the length of one side?
- A juice bottle holds 750 mL. How many such bottles fill a 9 L water tank?
- A classroom box measures 1.2 m by 0.8 m by 0.5 m. Find its volume in cubic metres and litres.
- V = 150×80×60 = 720,000 cm³ = 720,000 mL = 720 L.
- side = ³√216 = 6 cm.
- 9 L = 9000 mL; 9000 ÷ 750 = 12 bottles.
- V = 1.2×0.8×0.5 = 0.48 m³. In litres: 0.48×1000 = 480 L.
Try measuring some boxes and bottles at home. Write down their length, width and height, then calculate the volume. This helps you see how the formulas work in real life.