Understand the idea.
Translate the design question
A design model links the real object to measurable quantities. Identify fixed dimensions, variable dimensions and the decision being made. A labelled sketch helps translate a folding or filling process into a formula.
For a tray folded from corner cuts, the cut size becomes the height and is removed from both ends of each base dimension. For capacity, use internal lengths and the usable fill height rather than outside dimensions.
Interpret and test
Interpret the result against all stated constraints. Having enough volume does not guarantee that a box fits a height limit or that its material can be purchased in the required sheet sizes.
State assumptions such as negligible card thickness or a cylindrical interior. Keep exact values during calculations and ask whether a realistic change to an assumption would alter the design recommendation or reported capacity.
See the method in action.
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.
Worked solution
- 1
Find the folded base dimensions.
A strip is folded up at each end of both dimensions.
- 2
Identify the tray height.
The side walls rise by the size of the corner cut.
- 3
Calculate the interior volume under the stated model.
Ignoring thickness makes the tray a rectangular interior with these dimensions.
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.
Worked solution
- 1
Use the internal dimensions in the cylinder formula.
The given height is the usable water height and the radius is internal.
- 2
Convert cubic metres to litres.
Each cubic metre holds litres.
- 3
Round the final capacity.
Nearest-litre rounding is applied after conversion, with retained until evaluation.
9048 L
Try it yourself.
Check your understanding
A 20 by 16 cm card has 2 cm corner squares removed. Find tray base dimensions.
Show answer & reasoning
16 by 12 cm
Each base dimension loses two strips: and . The tray base is by .
Keep practising
6 worksheet questions · 14 marks
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.
.
560 cm³ - A box measures 40 by 25 by 12 cm internally. Find capacity.2 marks
cm³ 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
m².
.
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 ↗