The idea, step by step
Translate the design question
Identify what is fixed, what can vary and which constraint the design must meet. Draw a labelled sketch and choose internal dimensions when finding capacity. Write the formula before inserting numbers.
A large outside volume need not provide more usable space. Walls, openings and waste may matter; include them when the question specifies them.
Interpret and test
Check the number against the original aim. A box may have sufficient volume but fail a maximum-height limit, or require more whole sheets than an area calculation suggests.
State simplifying assumptions, then consider whether changing a realistic assumption would change the recommendation. Models support decisions rather than guaranteeing a perfect description.
A common trap
Using outside dimensions as exact usable capacity.
Instead: Use internal dimensions and the actual usable fill height.
See the thinking
Folded tray
Cut 3 cm squares from each corner of a 30 by 20 cm card and fold up the sides. Find volume, ignoring thickness.
- Base dimensions 30−6=24 and 20−6=14 cm; height 3 cm.
- Volume=3×24×14=1008 cm³.
Tank capacity
A cylinder has internal radius 1.2 m and usable water height 2 m. Estimate its capacity to the nearest litre.
- m³.
- Multiply by 1000 to obtain 9047.7868 L.
- Round at the end.
Check your understanding
A 20 by 16 cm card has 2 cm corner squares removed. Find tray base dimensions.
Show answer
16 by 12 cm
Each base dimension loses 2 cm at both ends.
Your turn
6 questions · 14 marks · Work at your own pace.
Read the questions online
- Cut 2 cm squares from a 24 by 18 cm card. Find folded tray volume.2 marks
- A box measures 40 by 25 by 12 cm internally. Find capacity.2 marks
- A cylinder has internal radius 1 m and usable height 1.5 m. Give exact litre capacity.2 marks
- Compare closed boxes 10 by 10 by 20 cm and 10 by 5 by 40 cm. Both hold 2000 cm³. Which uses less material?3 marks
- A design needs 2.4 m² plus 10% waste. Material costs 18 dollars per m². Find the continuous-area cost.2 marks
- A model uses outside dimensions but ignores 3 mm walls. Does it overestimate or underestimate usable capacity? Explain.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Cut 2 cm squares from a 24 by 18 cm card. Find folded tray volume.2 marks
Base 20 by 14; height 2.
V=560.
560 cm³ - A box measures 40 by 25 by 12 cm internally. Find capacity.2 marks
V=12000 cm³=12 L.
12 L - A cylinder has internal radius 1 m and usable height 1.5 m. Give exact litre capacity.2 marks
m³; multiply by 1000.
L - Compare closed boxes 10 by 10 by 20 cm and 10 by 5 by 40 cm. Both hold 2000 cm³. Which uses less material?3 marks
Their areas are 1000 and 1300 cm².
The 10 by 10 by 20 box. - A design needs 2.4 m² plus 10% waste. Material costs 18 dollars per m². Find the continuous-area cost.2 marks
Area=2.64 m².
2.64×18=47.52.
47.52 dollars - A model uses outside dimensions but ignores 3 mm walls. Does it overestimate or underestimate usable capacity? Explain.3 marks
Walls reduce the internal dimensions and occupy some outside volume.
Overestimate.
Curriculum reference & lesson scope
Australian Curriculum v9 and SA Curriculum
Surface area of composite solids; volume of composite solids; proportion/scaling of objects; related length/area/volume factors; measurement error; the effect of rounding and repeated approximations; practical design models; evaluating assumptions and suitable precision.
Official curriculum source ↗