The idea, step by step
Decide what the situation needs
Start by naming the requested quantity: boundary length, covering area, volume or capacity. Sketch the object and label only the dimensions that have been given. Identify a missing radius, height or cross-sectional area before choosing a formula.
Do one step at a time with units. For example, calculate a tank’s full internal volume first, convert to litres second, then calculate a percentage fill. Doing every step mentally makes unit mistakes harder to find.
Check the result before deciding
Compare an answer with an easy estimate and use the context. A paint order must cover the whole surface, so a fractional number of tins usually rounds up. A water tank’s usable capacity must exclude any unfilled space stated in the problem.
State assumptions such as uniform depth, negligible wall thickness or no overlap. A precise-looking number is not reliable if a needed dimension or a physical assumption is missing.
A common trap
Rounding down the number of packages because the decimal part looks small.
Instead: If the purchase must cover a requirement, round up to a whole package.
See the thinking
A partly filled tank
A tank has internal base area 5 m² and height 0.8 m. It is 75% full. How many litres of water does it contain?
- Full volume: m³.
- Full capacity: L.
- Water amount: L.
Buying enough material
A rectangular floor is 4 m by 3 m. Tiles cover 0.5 m² per box. Allow 10% extra area for cutting. How many whole boxes are needed?
- Floor area: m².
- Area with allowance: m².
- Boxes: .
- Buy 27 whole boxes, since 26 boxes are insufficient.
Check your understanding
A tank’s full capacity is 800 L. It is one-quarter full. How much water is in it?
Show answer
200 L.
One quarter of 800 is L.
Your turn
6 questions · 18 marks · Work at your own pace.
Read the questions online
- A rectangular bed is 6 m by 4 m. Soil is added to a uniform depth of 0.2 m. Find the soil volume.3 marks
- A 2 m³ tank is 60% full. Find the water volume in litres.3 marks
- A 3 m by 2 m rectangle is covered using sheets of area 0.8 m² each. Ignore overlap. Find the minimum number of whole sheets by area.3 marks
- A circular flowerbed has radius 2 m. A gardener doubles the radius. What happens to the area?3 marks
- A tank measures 1.2 m by 80 cm by 50 cm internally. Find its capacity in litres.4 marks
- A garden is shown only by a sketch with no scale or dimensions. Can its actual area be calculated? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A rectangular bed is 6 m by 4 m. Soil is added to a uniform depth of 0.2 m. Find the soil volume.3 marks
Base area: m².
Volume: m³.
4.8 m³. - A 2 m³ tank is 60% full. Find the water volume in litres.3 marks
Full capacity is 2000 L.
L.
1200 L. - A 3 m by 2 m rectangle is covered using sheets of area 0.8 m² each. Ignore overlap. Find the minimum number of whole sheets by area.3 marks
Area is 6 m².
, so at least 8 whole sheets are needed by area.
8 sheets. - A circular flowerbed has radius 2 m. A gardener doubles the radius. What happens to the area?3 marks
Old area is m².
New radius is 4 m, giving m².
The ratio is .
It becomes four times as large. - A tank measures 1.2 m by 80 cm by 50 cm internally. Find its capacity in litres.4 marks
Convert dimensions to metres: 1.2, 0.8 and 0.5.
Volume is m³.
Capacity is L.
480 L. - A garden is shown only by a sketch with no scale or dimensions. Can its actual area be calculated? Explain.2 marks
The same sketch could represent gardens of many sizes.
Measurements from an unscaled drawing do not determine actual lengths.
No. A scale or sufficient actual dimensions are needed.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum
Circumference and area of circles; perimeter/area of composite shapes; choosing and converting area units; cross-sections of prisms; prism volume and capacity; mixed measurement applications.
Official curriculum source ↗