Volume and Capacity of Right Prisms — AC9M8M02

• Use V=A_{cross-section}×length for right prisms.
• Convert correctly between cubic centimetres, cubic metres, millilitres and litres.
• Choose dimensions and capacity measures that answer a practical question.
• Combine volume with fill percentages or flow rates without mixing units.

Recall area formulas, metric length units, decimal multiplication, percentage of an amount and that 1 mL=1 cm³ and 1 L=1000 cm³.

A right prism has a constant cross-section. Imagine stacking identical slices: if each slice has area A and the stack extends a perpendicular length L, then V=AL. For a rectangular prism this becomes V=lwh.

Capacity describes how much a container can hold. The same physical space can be expressed using cubic units or liquid-capacity units: 1 cm³=1 mL, 1000 cm³=1 L and 1 m³=1000 L.

Preserve the AC9 practical contexts: packaging/production, fitting appliances into spaces, pool or tank capacity and combining dimensions with a filling rate.

• Multiplying three arbitrary dimensions. Identify the cross-section and the perpendicular prism length.
• Treating 1 m³ as 1000 cm³. Cubic conversion factors are cubed; 1 m³=1,000,000 cm³.
• Using litres before finding volume. Calculate a physical volume first, then convert if useful.
• Applying fill percentage to one length. Percentage full refers to volume/capacity unless the shape/context guarantees a linear height relationship.

1. Find the volume of a 12 cm×8 cm×5 cm rectangular prism.
2. Convert 4500 cm³ to litres.
3. Find a triangular-prism volume from a labelled cross-section.
4. Explain which measurements matter for fitting an appliance and which matter for capacity.

1. Find the volume of a prism with cross-section area 35 cm² and length 18 cm.
2. Convert 2.4 L to cm³.
3. Convert 0.75 m³ to litres.
4. A 90 L container is 60% full. How much does it contain?
5. Design a rectangular box with volume 2400 cm³ using integer dimensions.
6. A tank holds 3600 L and fills at 15 L/min. Find the fill time.
7. Explain one assumption in your fill-time model.

Two packaging designs have the same internal volume but different dimensions. Explain why equal capacity does not guarantee equal material use, storage efficiency or suitability for a shelf. Identify what extra measurements would be required to compare them fairly.

1. Why does V=A×L work for a right prism? The same cross-sectional area is repeated through a perpendicular length.
2. What is the link between cm³ and mL? 1 cm³=1 mL.
3. How many litres are in 1 m³? 1000 L.
4. Why keep dimensions and capacity separate in appliance problems? External dimensions determine fit; capacity describes usable internal space/load.

1. A right prism has trapezium cross-section area 48 cm² and length 25 cm. Find volume in cm³ and litres.
   Multiply area by prism length, then divide cm³ by 1000 for litres.
2. A 2.5 m×1.8 m×1.2 m tank is filled to 80%. Find water volume in litres.
   Find m³, multiply by 0.8, then use 1 m³=1000 L.
3. A 30 kL pool fills at 18 L/min. Estimate time and identify why the real time could differ.
   Convert kL to L; discuss changing flow, leakage or interruptions.

• I identify the cross-section and prism length.
• I convert cubic/capacity units correctly.
• I apply percentage to volume when appropriate.
• I state model assumptions.

Exit ticket: Why is 1 m³ much more than 100 cm³ even though 1 m=100 cm?

Australian Curriculum v9.0 — AC9M8M02: solve problems involving the volume and capacity of right prisms using appropriate units.

Victorian Curriculum F–10 Version 2.0 — Level 8, VC2M8M02: Exact.

NSW Mathematics K–10 Syllabus (2022) — Stage 4, MA4-VOL-C-01; MAO-WM-01: Exact for volume/capacity of right prisms, supported by Working mathematically.

• AC9M8M01 — composite area/perimeter
• AC9M8M05 — rates and unit rates

• Australian Curriculum v9.0
• Victorian Curriculum F–10 Version 2.0 Mathematics
• NSW Mathematics K–10 Syllabus (2022)

Curriculum equivalents for Solve problems involving the volume and capacity of right prisms...

Mapped skill: solve problems involving the volume and capacity of right prisms using 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.

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.