Australian Curriculum v9 / ACiQ Year 8 Mathematics - Unit 3 - Right-prism volume and capacity

Right-prism volume and capacity

Calculate volumes of right prisms and connect cubic units with practical capacity.

Updated 2026-07-26 - 12 min read

Right-prism volume and capacity is taught here as a connected set of decisions, not a list of facts. Work through the prerequisite recall, explicit models, carefully faded examples, misconception repairs and transfer task before using the target in Check, Practice, Review or Rapid Revision.

This note is designed to work with the guided lessons, curated practice, flashcards, Tutor context, Review and Rapid Revision for the same canonical target. The same three evidence checks are used throughout, so feedback can route a learner back to the precise idea that needs repair.

Use cross-sectional area for prism volume

A right prism's volume equals the area of its constant cross-section multiplied by the perpendicular length. This relationship must be selected from the quantities and conditions in the problem, then checked against the context.

A dependable reasoning routine

  1. Name the unknowns, units and constraints before calculating.
  2. Choose the relationship represented by use cross-sectional area for prism volume and state why it applies.
  3. Keep exact values for as long as possible, show substitutions and preserve units through each step.
  4. Check the result by substitution, estimation, an alternative representation or the original context.

Repair: Volume measures three-dimensional space, so a rectangular prism uses length × width × height and a general prism uses cross-sectional area × length.

The repair matters because the shortcut may appear to work in one familiar example while failing when the method, representation, scale, constraint or accuracy requirement changes. Use the routine above to make the reasoning visible enough for another learner to verify.

Example 1.1

Find the volume of a rectangular prism 8 cm by 5 cm by 3 cm.

Step 1 - identify the governing idea: A right prism's volume equals the area of its constant cross-section multiplied by the perpendicular length.

Step 2 - apply it to this evidence: Multiplying the three perpendicular dimensions gives 8 × 5 × 3 = 120.

Result: 120 cm³

The relationship is visible in the working: Multiplying the three perpendicular dimensions gives 8 × 5 × 3 = 120. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 16 cm³ — It does not agree with the required relationship: Multiplying the three perpendicular dimensions gives 8 × 5 × 3 = 120.
  • 40 cm³ — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 240 cm³ — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 1.2

A triangular prism has cross-sectional area 24 cm² and length 10 cm. Find its volume.

Step 1 - identify the governing idea: A right prism's volume equals the area of its constant cross-section multiplied by the perpendicular length.

Step 2 - apply it to this evidence: Volume is 24 cm² × 10 cm.

Result: 240 cm³

The relationship is visible in the working: Volume is 24 cm² × 10 cm. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 34 cm³ — It does not agree with the required relationship: Volume is 24 cm² × 10 cm.
  • 120 cm³ — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 480 cm³ — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 1.3

A prism has volume 360 m³ and cross-sectional area 45 m². Find its length.

Step 1 - identify the governing idea: A right prism's volume equals the area of its constant cross-section multiplied by the perpendicular length.

Step 2 - apply it to this evidence: Rearranging V = Al gives l = 360 ÷ 45 = 8.

Result: 8 m

The relationship is visible in the working: Rearranging V = Al gives l = 360 ÷ 45 = 8. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 16 m — It does not agree with the required relationship: Rearranging V = Al gives l = 360 ÷ 45 = 8.
  • 405 m — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 0.125 m — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Convert volume and capacity

Use 1 cm³ = 1 mL and 1000 cm³ = 1 L, while metric length conversions must be cubed when converting cubic units. This relationship must be selected from the quantities and conditions in the problem, then checked against the context.

A dependable reasoning routine

  1. Name the unknowns, units and constraints before calculating.
  2. Choose the relationship represented by convert volume and capacity and state why it applies.
  3. Keep exact values for as long as possible, show substitutions and preserve units through each step.
  4. Check the result by substitution, estimation, an alternative representation or the original context.

Repair: One millilitre equals one cubic centimetre; one litre equals 1000 cubic centimetres.

The repair matters because the shortcut may appear to work in one familiar example while failing when the method, representation, scale, constraint or accuracy requirement changes. Use the routine above to make the reasoning visible enough for another learner to verify.

Example 2.1

Convert 2500 cm³ to litres.

Step 1 - identify the governing idea: Use 1 cm³ = 1 mL and 1000 cm³ = 1 L, while metric length conversions must be cubed when converting cubic units.

Step 2 - apply it to this evidence: Since 1000 cm³ = 1 L, divide by 1000.

Result: 2.5 L

The relationship is visible in the working: Since 1000 cm³ = 1 L, divide by 1000. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 2500 L — It does not agree with the required relationship: Since 1000 cm³ = 1 L, divide by 1000.
  • 25 L — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 0.25 L — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 2.2

A tank holds 18 L. What is this in cubic centimetres?

Step 1 - identify the governing idea: Use 1 cm³ = 1 mL and 1000 cm³ = 1 L, while metric length conversions must be cubed when converting cubic units.

Step 2 - apply it to this evidence: Each litre is 1000 cm³, so 18 × 1000 = 18000.

Result: 18000 cm³

The relationship is visible in the working: Each litre is 1000 cm³, so 18 × 1000 = 18000. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 180 cm³ — It does not agree with the required relationship: Each litre is 1000 cm³, so 18 × 1000 = 18000.
  • 1800 cm³ — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 0.018 cm³ — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 2.3

Convert 0.006 m³ to litres.

Step 1 - identify the governing idea: Use 1 cm³ = 1 mL and 1000 cm³ = 1 L, while metric length conversions must be cubed when converting cubic units.

Step 2 - apply it to this evidence: One cubic metre is 1000 L, so 0.006 × 1000 = 6.

Result: 6 L

The relationship is visible in the working: One cubic metre is 1000 L, so 0.006 × 1000 = 6. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 0.006 L — It does not agree with the required relationship: One cubic metre is 1000 L, so 0.006 × 1000 = 6.
  • 60 L — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 6000 L — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Solve practical prism-capacity problems

Model the internal dimensions, calculate usable volume and convert units before comparing with the required capacity. This relationship must be selected from the quantities and conditions in the problem, then checked against the context.

A dependable reasoning routine

  1. Name the unknowns, units and constraints before calculating.
  2. Choose the relationship represented by solve practical prism-capacity problems and state why it applies.
  3. Keep exact values for as long as possible, show substitutions and preserve units through each step.
  4. Check the result by substitution, estimation, an alternative representation or the original context.

Repair: Capacity is the internal space, so wall thickness or unfilled space must be accounted for when relevant.

The repair matters because the shortcut may appear to work in one familiar example while failing when the method, representation, scale, constraint or accuracy requirement changes. Use the routine above to make the reasoning visible enough for another learner to verify.

Example 3.1

A rectangular tank is 80 cm by 50 cm by 40 cm internally. Find capacity.

Step 1 - identify the governing idea: Model the internal dimensions, calculate usable volume and convert units before comparing with the required capacity.

Step 2 - apply it to this evidence: The volume is 160000 cm³, which equals 160 L.

Result: 160 L

The relationship is visible in the working: The volume is 160000 cm³, which equals 160 L. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 160000 L — It does not agree with the required relationship: The volume is 160000 cm³, which equals 160 L.
  • 170 L — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 16 L — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 3.2

A 12 L container is filled to 75%. How much liquid is inside?

Step 1 - identify the governing idea: Model the internal dimensions, calculate usable volume and convert units before comparing with the required capacity.

Step 2 - apply it to this evidence: 0.75 × 12 L = 9 L.

Result: 9 L

The relationship is visible in the working: 0.75 × 12 L = 9 L. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 3 L — It does not agree with the required relationship: 0.75 × 12 L = 9 L.
  • 16 L — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 900 L — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Example 3.3

A prism-shaped trough has cross-sectional area 0.18 m² and length 2.5 m. What is its capacity?

Step 1 - identify the governing idea: Model the internal dimensions, calculate usable volume and convert units before comparing with the required capacity.

Step 2 - apply it to this evidence: Volume is 0.45 m³, and 0.45 m³ = 450 L.

Result: 450 L

The relationship is visible in the working: Volume is 0.45 m³, and 0.45 m³ = 450 L. Check the units and substitute or estimate where possible. A plausible-looking number is not enough unless it satisfies the original conditions.

Why the alternatives fail:

  • 45 L — It does not agree with the required relationship: Volume is 0.45 m³, and 0.45 m³ = 450 L.
  • 0.72 L — It changes or misses a condition in the question. Reapply the relationship and retain the stated units or accuracy.
  • 4500 L — A substitution, estimate, ordering or unit check rejects this result; it does not reproduce the conditions in the prompt.

Retrieval check

Try these without looking back at the examples.

  1. A triangular prism has cross-sectional area 24 cm² and length 10 cm. Find its volume.
  2. A tank holds 18 L. What is this in cubic centimetres?
  3. A 12 L container is filled to 75%. How much liquid is inside?

Answers

  1. 240 cm³ — Volume is 24 cm² × 10 cm.
  2. 18000 cm³ — Each litre is 1000 cm³, so 18 × 1000 = 18000.
  3. 9 L — 0.75 × 12 L = 9 L.

Transfer task

Find an unfamiliar example from school, daily life, a credible news source or another subject. Explain which of the three evidence checks applies. Complete the task, then audit your own response: identify the evidence used, the relationship applied, one plausible misconception and the final reasonableness check. If a peer could not reproduce your reasoning, add the missing step.

Sources