Grade 7 Mathematics MEASUREMENT – Volume and capacity Notes
MEASUREMENT — Volume and Capacity
Subject: Mathematics | Subtopic: Volume and Capacity | Age: 12 (Kenya)
What are volume and capacity?
- Volume is the amount of space inside a 3D object (for example, inside a box or a water tank). We measure it in cubic units such as cubic centimetres (cm³), cubic metres (m³).
- Capacity is how much a container can hold, usually measured in litres (L) or millilitres (mL). Capacity is often used for liquids.
Important relationships (metric):
- 1 cubic centimetre (1 cm³) = 1 millilitre (1 mL)
- 1 000 millilitres (1 000 mL) = 1 litre (1 L)
- 1 cubic decimetre (1 dm³) = 1 litre (1 L)
- 1 cubic metre (1 m³) = 1 000 litres (1 000 L)
- 1 m³ = 1 000 000 cm³
l
w
h
Rectangular box (cuboid)
Cylinder (e.g. water tank)
Formulas for volume
- Cube (side = a): V = a³ (units: cm³, m³)
- Rectangular prism / Cuboid (length l, width w, height h): V = l × w × h
- Cylinder (radius r, height h): V = π r² h (use π ≈ 3.14)
Worked examples
Example 1 — Cuboid
A water tank shaped like a cuboid is 2 m long, 1.2 m wide and 0.8 m high. Find its volume in cubic metres and its capacity in litres.
A water tank shaped like a cuboid is 2 m long, 1.2 m wide and 0.8 m high. Find its volume in cubic metres and its capacity in litres.
Volume = l × w × h = 2 × 1.2 × 0.8 = 1.92 m³.
Capacity in litres: 1 m³ = 1000 L, so 1.92 m³ = 1.92 × 1000 = 1920 L.
Capacity in litres: 1 m³ = 1000 L, so 1.92 m³ = 1.92 × 1000 = 1920 L.
Example 2 — Cylinder
A cylindrical jerrycan has a radius of 7 cm and height 30 cm. Find the volume in cm³ and convert to litres.
A cylindrical jerrycan has a radius of 7 cm and height 30 cm. Find the volume in cm³ and convert to litres.
V = π r² h ≈ 3.14 × 7² × 30 = 3.14 × 49 × 30 = 3.14 × 1470 ≈ 4615.8 cm³.
Since 1 cm³ = 1 mL, this is ≈ 4615.8 mL ≈ 4.616 L (divide by 1000).
Since 1 cm³ = 1 mL, this is ≈ 4615.8 mL ≈ 4.616 L (divide by 1000).
Conversions quick guide
- cm³ → mL : same number (500 cm³ = 500 mL)
- mL → L : divide by 1000 (1500 mL = 1.5 L)
- m³ → L : multiply by 1000 (0.75 m³ = 750 L)
- cm³ → m³ : divide by 1 000 000 (2 000 000 cm³ = 2 m³)
Tips and checks
- Always use consistent units before calculating (convert cm to m if mixing units).
- When answering capacity questions, give the unit (L or mL) clearly.
- Use 3.14 for π unless your teacher asks for more accuracy.
- Draw the shape and label l, w, h or r and h before substituting values.
Practice questions
- A cube has side 12 cm. Find its volume in cm³ and litres.
- A rectangular tank is 150 cm long, 80 cm wide and 120 cm high. What is its volume in m³ and its capacity in litres?
- A cylindrical drum has radius 0.35 m and height 0.9 m. Find its volume in litres (use π = 3.14).
- Convert 2.5 m³ to litres. Convert 3 600 mL to litres.
Answers
- V = 12³ = 1728 cm³ = 1728 mL = 1.728 L.
- Volume (cm³) = 150 × 80 × 120 = 1 440 000 cm³ = 1.44 m³. Capacity = 1.44 × 1000 = 1440 L.
- V = π r² h ≈ 3.14 × 0.35² × 0.9 = 3.14 × 0.1225 × 0.9 ≈ 0.3465 m³ = 346.5 L (since 1 m³ = 1000 L).
- 2.5 m³ = 2.5 × 1000 = 2500 L. 3 600 mL = 3.6 L.
Remember: Volume measures space (use cubic units). Capacity measures how much a container can hold (use litres and millilitres). In Kenya you will mostly use metric units — cm³, m³, L and mL.
Prepared for classroom revision — short and clear notes to help practise problems you may meet in Kenyan primary/early secondary assessments.