Add prism faces and remove only the faces that are absent
Calculate a cuboid surface area from its six faces · Use 2A+PL for a closed right prism · Adapt a face count for an open container
Section Paper 4 · Historical Extended · calculator
Exam scope and assessment notes
Core and Extended foundations. Historical study of Cambridge IGCSE Mathematics (US) 0444, 2025 Version 2. The final assessment was June 2025; the syllabus was available only to schools in Arizona, USA. This is not a current exam-entry option. Original self-check teaching and explained practice are not Cambridge papers, official marks or predicted grades. Linked teaching foundations do not establish full syllabus mastery. Calibrated cumulative assessment, reliable drawn-work review and qualified mathematics-teacher review remain unfinished.
Before you begin
- Prism volume
- Plane area and perimeter
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should you establish before applying the method in this lesson?
What you will learn
- Calculate a cuboid surface area from its six faces
- Use 2A+PL for a closed right prism
- Adapt a face count for an open container
A net accounts for faces
A closed cuboid has pairs of l by w, l by h and w by h rectangles: surface area 2(lw+lh+wh). For a closed right prism, the two ends have total area 2A and the rectangular side faces total PL, where P is the cross-section perimeter and L the prism length. This side-face rule assumes a right prism.
An opening changes the face list
An open box with no lid has one fewer rectangle than a closed box. List the actual exposed faces rather than blindly applying the closed formula. Volume measures the interior capacity or material amount; surface area measures coating or sheet requirements. State whether wall thickness, overlaps and waste are ignored.
Sources for this lesson
Pause and explain
How does removing only the lid change a cuboid surface area?
Worked example
Find the total surface area of a closed 6 cm by 4 cm by 3 cm cuboid.
Show the worked solution
- Face pairs have areas 24, 18 and 12 cm².
- Double their sum: 2(24+18+12).
Answer 108 cm².
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Find the surface area of a closed cuboid 5 cm by 3 cm by 2 cm.
Give me a hint
Count each rectangular face pair.
Compare my reasoning
- Areas are 15, 10 and 6 cm².
- Surface area=2(15+10+6)=62 cm².
62 cm².
Look for these in your work
- Include all six faces
- Use square units
A right triangular prism has cross-section sides 3, 4, 5 cm, perpendicular legs 3 and 4 cm, and length 10 cm. Find its closed surface area.
Give me a hint
Use section area 6 and perimeter 12.
Compare my reasoning
- Two triangular ends give 12 cm².
- Side faces give 12×10=120 cm²; total=132 cm².
132 cm².
Look for these in your work
- Distinguish area from perimeter
- Include both ends
A thin open-top box has base 8 cm by 5 cm and vertical height 3 cm. Find its sheet area, ignoring thickness, joins and waste.
Give me a hint
Include the base and four sides.
Compare my reasoning
- Base=40 cm²; side pairs total 2(8×3)+2(5×3)=78 cm².
- Sheet area=40+78=118 cm².
118 cm².
Look for these in your work
- Count the actual faces
- State the modelling assumptions
Common mistakes
- Do not multiply three lengths for a surface area.
- Identify the actual missing face in an open box.
What can you explain now?
How does removing only the lid change a cuboid surface area?
Compare with the explanation
Subtract that lid area once.
Only one of the six faces is absent.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
How does removing only the lid change a cuboid surface area?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.