Example 1
Rectangular-prism volume
- Identify dimensions 8 cm, 5 cm and 3 cm.
- Find cross-section area 8×5=40 cm².
- Multiply by prism length 3 cm.
- State cubic units.
Final answer: 120 cm³
Check: Three layers of 40 cm³ total 120 cm³.
What students learn in AC9M7M02
We are learning to solve problems involving the volume of right prisms, including rectangular and triangular prisms, using established formulas and appropriate units.
A right prism repeats an unchanged cross-section through a perpendicular length, so its volume is cross-section area multiplied by prism length.
For rectangular cross-sections use lw; for triangular cross-sections use ½bh before multiplying by the prism length. Volume requires cubic units.
Volume models capacity when conversion factors are applied explicitly, such as 1000 cm³=1 L. Verify a triangular prism as half an enclosing rectangular prism.
Success criteria
- I can identify a prism cross-section and perpendicular length.
- I can calculate rectangular and triangular prism volumes.
- I can convert capacity units and verify a volume independently.
Key vocabulary
- right prism
- solid with congruent parallel cross-sections joined perpendicularly.
- cross-section
- face or slice perpendicular to prism length.
- volume
- three-dimensional space occupied.
Visual models and representations
Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.
4 worked numerical & application examples
Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.
Example 2
Triangular-prism volume
- Find cross-section area ½×6×4=12 cm².
- Identify prism length 10 cm.
- Use V=cross-section area×length.
- Calculate 12×10.
Final answer: 120 cm³
Check: It is half a 6×4×10 rectangular prism: 240÷2=120.
Example 3
Application problem 1
Problem: A triangular prism has triangular cross-section base 6 cm, perpendicular height 4 cm and prism length 10 cm. Find its volume and explain why multiplying 6×4×10 directly is wrong.
- Plan: Represent the information first, then calculate, interpret and independently check the result.
- Work: Cross-section area = 1/2×6×4 = 12 cm², so volume = 12×10 = 120 cm³. Direct multiplication misses the 1/2 in the triangle area.
- Interpret: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Final answer: Cross-section area = 1/2×6×4 = 12 cm², so volume = 12×10 = 120 cm³. Direct multiplication misses the 1/2 in the triangle area.
Check: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Example 4
Application problem 2
Problem: A triangular prism has volume 360 cm³, triangle base 12 cm and height 5 cm. Find length.
- Plan: Divide by cross-section area 30 cm².
- Work: The triangular cross-section is ½×12×5=30 cm², so the prism length is 360÷30=12 cm; checking gives 30×12=360 cm³.
- Interpret: The complete model for “A triangular prism has volume 360 cm³, triangle base 12 cm and height 5 cm. Find length.” shows The triangular cross-section is ½×12×5=30 cm², so the prism length is 360÷30=12 cm; checking gives 30×12=360 cm³.
Final answer: The triangular cross-section is ½×12×5=30 cm², so the prism length is 360÷30=12 cm; checking gives 30×12=360 cm³.
Check: The complete model for “A triangular prism has volume 360 cm³, triangle base 12 cm and height 5 cm. Find length.” shows The triangular cross-section is ½×12×5=30 cm², so the prism length is 360÷30=12 cm; checking gives 30×12=360 cm³.
Common misconceptions
Common mistake: All three visible edges multiplied for a triangular prism.
Correction: Find triangular area first.
Common mistake: Square units used for volume.
Correction: Use cubic units.
Common mistake: Prism length confused with triangle height.
Correction: Label each perpendicular dimension.
10 important problems to solve
Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.
1. Find the volume of a 4×3×5 cm rectangular prism.
Check answer
Answer: 60 cm³.
Hint: Multiply all three perpendicular dimensions.
Why: Using the method “Multiply all three perpendicular dimensions.” gives 60 cm³.
2. A prism has cross-section 12 cm² and length 7 cm. Find its volume.
Check answer
Answer: 84 cm³.
Hint: Multiply cross-section area by length.
Why: Using the method “Multiply cross-section area by length.” gives 84 cm³.
3. Convert 2000 cm³ to litres.
Check answer
Answer: 2 L.
Hint: Divide by 1000.
Why: Using the method “Divide by 1000.” gives 2 L.
4. A triangular prism has triangle base 8 cm, height 5 cm and length 9 cm. Find volume.
Check answer
Answer: 180 cm³.
Hint: Find triangle area before multiplying by length.
Why: Using the method “Find triangle area before multiplying by length.” gives 180 cm³.
5. A prism volume is 240 cm³ and cross-section area is 30 cm². Find length.
Check answer
Answer: 8 cm.
Hint: Divide volume by cross-section area.
Why: Using the method “Divide volume by cross-section area.” gives 8 cm.
6. Convert 1.5 L to cubic centimetres.
Check answer
Answer: 1500 cm³.
Hint: Multiply litres by 1000.
Why: Using the method “Multiply litres by 1000.” gives 1500 cm³.
7. Explain why V=½bhL for a triangular prism.
Check answer
Answer: The factor ½bh calculates the triangular cross-section area, and multiplying by L extends that unchanged cross-section through the prism, giving V=½bhL.
Hint: Identify the repeated face.
Why: The reasoning for “Explain why V=½bhL for a triangular prism.” is complete because The factor ½bh calculates the triangular cross-section area, and multiplying by L extends that unchanged cross-section through the prism, giving V=½bhL.
8. A 2.4 m×1.5 m×0.5 m tank is 80% full. Find water volume.
Check answer
Answer: The full tank volume is 2.4×1.5×0.5=1.8 m³; 80% full means 0.80×1.8=1.44 m³ of water.
Hint: Find full volume, then take 80%.
Why: The complete model for “A 2.4 m×1.5 m×0.5 m tank is 80% full. Find water volume.” shows The full tank volume is 2.4×1.5×0.5=1.8 m³; 80% full means 0.80×1.8=1.44 m³ of water.
9. A triangular prism has volume 360 cm³, triangle base 12 cm and height 5 cm. Find length.
Check answer
Answer: The triangular cross-section is ½×12×5=30 cm², so the prism length is 360÷30=12 cm; checking gives 30×12=360 cm³.
Hint: Divide by cross-section area 30 cm².
Why: The complete model for “A triangular prism has volume 360 cm³, triangle base 12 cm and height 5 cm. Find length.” shows The triangular cross-section is ½×12×5=30 cm², so the prism length is 360÷30=12 cm; checking gives 30×12=360 cm³.
10. A triangular prism has triangular cross-section base 6 cm, perpendicular height 4 cm and prism length 10 cm. Find its volume and explain why multiplying 6×4×10 directly is wrong.
Check answer
Answer: Cross-section area = 1/2×6×4 = 12 cm², so volume = 12×10 = 120 cm³. Direct multiplication misses the 1/2 in the triangle area.
Hint: Represent the information first, then calculate, interpret and independently check the result.
Why: This synthesis problem combines the chapter's core representation, calculation and reasoning skills.
Curriculum coverage and elaborations
Content description: solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units.
International curriculum mapping
The Australian Curriculum code above is exact. Victorian Year 7, NSW Stage 4, US Grade 7, England Key Stage 3, New Zealand Level 4 and comparable international curricula contain broadly related learning, but code-to-code equivalence varies by jurisdiction.
🎥 Optional Video Lesson
The SkillrHub lesson remains the primary learning resource. This optional video reinforces the explanation; you can complete the lesson and practice without watching.
Before you watch:
- Pause after each worked example.
- Try the examples yourself.
- Return to the SkillrHub lesson before continuing.
Recommended: Find the Volume of a Triangular Prism and Cube
Khan Academy — Use the area of a prism’s cross-section and its length to find volume.
As you watch: Why does multiplying the cross-sectional area by the prism length give cubic units?
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Try it: Find the volume of a triangular prism with triangle base 4 cm, perpendicular height 3 cm and length 8 cm.
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Curriculum equivalents: Victoria, NSW and international
Curriculum equivalents for Solve problems involving the volume of right prisms including rectangular...
Mapped skill: solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units
These references identify matching or closely related learning. Curriculum sequence, terminology and depth vary, so teachers should use the mapped skill and lesson difficulty to confirm suitability.
| Region | Curriculum framework | Closest level or code |
|---|---|---|
| Australia | Australian Curriculum v9.0 | AC9M7M02 · Year 7 |
| Victoria | Victorian Curriculum F–10 Version 2.0 — Mathematics | VC2M7M02 · Level 7 |
| New South Wales | NSW Mathematics K–10 Syllabus (2022) | MA4-VOL-C-01 · Stage 4 |
| United States (USA) | Common Core State Standards for Mathematics | Grade 7 |
| Canada (Ontario) | Ontario Curriculum — Mathematics | Grade 7 |
| United Kingdom (England) | National Curriculum in England — Mathematics | Year 8, Key Stage 3 |
| India | NCERT / CBSE — Mathematics | Class 7 |
Australian Curriculum v9.0 is the canonical source for this SkillrHub lesson. Victoria and NSW entries name the closest published state codes or outcomes; international entries are planning references rather than claims of identical curricula.
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Topic reference: AC9M7M02 — Volume of Right Prisms
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