Year 7 Mathematics · AC9M7M02

Volume of Right Prisms

We are learning to solve problems involving the volume of right prisms, including rectangular and triangular prisms, using established formulas and appropriate units

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Learning goalsSay it simply

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 conceptTeach from the board

Use these models to connect the mathematical idea to values, diagrams, coordinates, graphs or structure before moving to symbolic calculation.

Follow each example from representation and setup through calculation/reasoning, interpretation and an independent check.

Example 1

Rectangular-prism volume

  1. Identify dimensions 8 cm, 5 cm and 3 cm.
  2. Find cross-section area 8×5=40 cm².
  3. Multiply by prism length 3 cm.
  4. State cubic units.

Final answer: 120 cm³

Check: Three layers of 40 cm³ total 120 cm³.

Example 2

Triangular-prism volume

  1. Find cross-section area ½×6×4=12 cm².
  2. Identify prism length 10 cm.
  3. Use V=cross-section area×length.
  4. 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.

  1. Plan: Represent the information first, then calculate, interpret and independently check the result.
  2. 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.
  3. 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.

  1. Plan: Divide by cross-section area 30 cm².
  2. 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.
  3. 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.

Clean visual examplesOne-page board

Clean one-page examples

AC9M7M02 - Volume of Right Prisms
Example 1

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.

Example 2

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

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

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.

Curriculum examplesCopied content

Content description: solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units.

Questions and answersWith answers

Attempt each problem before opening Check answer. The set moves from core understanding to application and synthesis.

  1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.

Practice and reviewReady for practice

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.

Curriculum alignmentStart here

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.
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