Calculate prism volume from a constant cross-sectional area
Recognise a constant cross section · Use cross-sectional area times perpendicular length · Distinguish a prism from a tapering solid
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
- Plane areas
- Cubic units
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
- Recognise a constant cross section
- Use cross-sectional area times perpendicular length
- Distinguish a prism from a tapering solid
Stack equal sections
A prism has the same cross-sectional shape and area along its length. Volume is cross-sectional area A times the perpendicular distance L between its parallel ends: V=AL. For a right prism, that distance is its straight length. For a cuboid, V=lwh.
A triangular prism with a right-triangle section of legs 3 cm and 4 cm has A=6 cm². A length of 10 cm gives volume 60 cm³. The sloping triangle side is not used as its perpendicular height.
Check the model
A solid that narrows from a base to an apex is not a constant-section prism. Its base area times height would overestimate its volume. Convert all dimensions to compatible units before multiplying; the final volume uses cubic units.
Sources for this lesson
Pause and explain
What is the volume of a prism with section area 12 cm² and perpendicular length 5 cm?
Worked example
Find the volume of a right triangular prism with perpendicular section legs 3 cm and 4 cm, length 10 cm.
Show the worked solution
- Section area=(1/2)×3×4 = 6 cm².
- Volume=6×10 = 60 cm³.
Answer 60 cm³.
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 volume of a cuboid 6 cm by 4 cm by 3 cm.
Give me a hint
Multiply its three perpendicular dimensions.
Compare my reasoning
- Base area=6×4=24 cm².
- Volume=24×3=72 cm³.
72 cm³.
Look for these in your work
- Use compatible units
- Write a cubic unit
A right prism has a trapezoid section with parallel sides 4 cm and 8 cm, separation 3 cm, and prism length 10 cm. Find its volume.
Give me a hint
Find the cross-sectional area first.
Compare my reasoning
- Area=(4+8)×3/2 = 18 cm².
- Volume=18×10 = 180 cm³.
180 cm³.
Look for these in your work
- Choose the section height
- Then use the prism length
A prism of volume 240 cm³ has constant cross-sectional area 30 cm². Find its perpendicular length. Would the same equation apply unchanged to a tapering pyramid?
Give me a hint
Rearrange V=AL and check its condition.
Compare my reasoning
- L=240/30=8 cm.
- A pyramid has changing sections, so this prism equation does not apply unchanged.
8 cm; no, the pyramid is not a constant-section prism.
Look for these in your work
- Reverse the formula
- State its geometric condition
Common mistakes
- Use the perpendicular section height.
- Check that the cross-sectional area is constant.
What can you explain now?
What is the volume of a prism with section area 12 cm² and perpendicular length 5 cm?
Compare with the explanation
60 cm³.
Multiply the area by the length.
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Make it stick
What is the volume of a prism with section area 12 cm² and perpendicular length 5 cm?
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.