Year 8 Mathematics · AC9M8M02

Volume and Capacity of Right Prisms

A right prism repeats one cross-section through a perpendicular length, so volume equals cross-sectional area × prism length. Connect cubic units to capacity units before…

Ready to project and teach

Key conceptTeach from the board

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.

Worked examplesWe do

Worked examples

AC9M8M02 - Volume and Capacity of Right Prisms
Example 1

Find the volume of a 12 cm×8 cm×5 cm rectangular prism.

Example 2

Convert 4500 cm³ to litres.

Example 3

Find a triangular-prism volume from a labelled cross-section.

Example 4

Explain which measurements matter for fitting an appliance and which matter for capacity.

Curriculum examplesCopied content

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.

LessonAC v9VictoriaNSW
Right-prism volume/capacityAC9M8M02VC2M8M02 — ExactMA4-VOL-C-01; MAO-WM-01 — Exact
Questions and answersWith answers
  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.
Practice and reviewReady for practice
  • 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.
Curriculum alignmentStart here
Related resourcesKeep teaching
Teach & ExplainTeaching slides and samples

Teach this topic step by step

Explore optional teaching slide packs for classroom lessons and explanations at home.

Browse Teach & Explain · Browse Print & Go

Teachers: follow SkillrHub on TPT, then email us to request a free sample before buying. Include the year, subject and topic or curriculum code.

Request a free sample

After trying the sample, honest feedback is welcome. A TPT review is optional, where available, and does not need to be positive.