Area, volume and units
Build a rectangular prism from layers and keep square and cubic units distinct.
Before you begin
- Rectangle area
- Multiplication and unit conversions
Measure a surface with square units
Area counts how many unit squares cover a surface without overlap. A rectangle of length l and width w has area lw. Both lengths must use the same unit before multiplication. A 1 m square contains 100 × 100 = 10,000 square centimetres; converting area requires squaring the length conversion factor.
Build volume from equal layers
Volume measures occupied three-dimensional space. A rectangular prism has l × w cubes in one unit-high layer and h such layers, so V = lwh. If lengths are in centimetres, volume is in cubic centimetres. One cubic centimetre has the same volume as one millilitre. An open container's capacity uses its internal dimensions.
Worked example
A box has internal dimensions 8 cm by 5 cm by 3 cm. Find its capacity.
Show the worked solution
- The base area is 8 × 5 = 40 cm².
- Three centimetres of height gives 40 × 3 = 120 cm³.
- Use 1 cm³ = 1 mL to express the internal capacity.
120 cm³, or 120 mL.
Try it yourself
A 4 cm by 3 cm rectangle has which area?
Common mistakes
- Convert all lengths to the same unit before multiplying.
- Surface area and volume answer different questions.
What can you explain now?
A tank has internal dimensions 20 cm by 10 cm by 15 cm. How many litres does it hold?
Compare with the explanation
3 litres.
Volume is 20 × 10 × 15 = 3,000 cm³ = 3,000 mL. Divide millilitres by 1,000 to get litres.
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Original StudyForA content. AI-assisted checks completed; subject-teacher review is still pending. These lessons are not endorsed by an exam board.
Common Core mathematics standards ↗