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# Volume and capacity

Area, volume, circles and Pythagoras · Volume

<!-- Speaker note: Students build boxes and tanks, read their volume and capacity together, and convert between cm³, mL, L and m³ (AC9M8M02, node 1). About 35 minutes (Predict and Run 8 min · Investigate 8 min · Modify 10 min · Practise and Make 9 min). -->

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## Today

**We are learning to** volume measures space in cubic units; capacity measures how much a container holds. 1 cm³ holds 1 mL, 1000 cm³ holds 1 L, and 1 m³ holds 1000 L. A cubic metre is 100 × 100 × 100 = 1 000 000 cm³, not 100.

- I can convert between cm³, mL, L and m³.
- I can explain why 1 m³ is 1 000 000 cm³.
- I can choose a sensible unit for a container.

<!-- Speaker note: Before class: Do the Run board yourself first. Bring a 1 L carton and a 10 cm cube (or a drawing) if you can. The one idea: 1 cm³ holds 1 mL, so 1000 cm³ is 1 L, and 1 m³ (100 × 100 × 100 cm³) is 1000 L. The common mistake is converting a cubic unit with the length factor once (Ravi's mistake). The board gives capacity in mL or L for cm and in L for m. Wider: why a cubic metre of water has a mass of about a tonne, and water storage in kilolitres or megalitres (dams, town water). -->

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## Why it matters

> A 1 L milk carton and a 10 cm cube hold exactly the same amount. A cubic metre of water is a tonne. Why do the units fit together so neatly?

<!-- Speaker note: **Volume** is the space a solid takes up, in cubic units (cm³, m³). **Capacity** is how much a container holds, in millilitres (mL), litres (L) or kilolitres (kL). They link exactly: | Volume | Capacity | |---|---| | 1 cm³ | 1 mL | | 1000 cm³ (a 10 cm cube) | 1 L | | 1 m³ | 1000 L = 1 kL | A cubic metre is 100 cm × 100 cm × 100 cm = **1 000 000 cm³**: a length conversion is used three times, once for each direction. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Predict

**A box is 10 cm by 10 cm by 10 cm. How much water does it hold?**

- 1 L
- 10 L
- 100 mL
- 1000 L

<!-- Speaker note: What happens: 1 L. 10 × 10 × 10 = 1000 cm³, and each cm³ holds 1 mL: 1000 mL = 1 L. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: ask students to show the size of a litre with their hands. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Fmeasurement%2Fvolume-and-capacity%2Fstep-2&code=widget%3A+prism%0Abase%3A+rectangle%0Aslider+l%3A+1%2C+12%2C+4%0Aslider+w%3A+1%2C+12%2C+5%0Aslider+h%3A+0%2C+12%2C+2%0Aunits%3A+cm%0Acapacity%3A+on%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/measurement/volume-and-capacity/?full=step-2#step-2)

<!-- Speaker note: The panel gives the volume and the capacity together. -->

<!-- Speaker note: Teacher: ask for two different boxes that hold 1 L. -->

<style scoped>pre, marp-pre { font-size: 0.5em; line-height: 1.25; } section { font-size: 25px; }</style>

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What happened?

* 1 L. 10 × 10 × 10 = 1000 cm³, and each cm³ holds 1 mL: 1000 mL = 1 L.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Cubic metres

**How many litres does 1 m³ hold?**

* Answer: 1000

<!-- Speaker note: 1 m³ = 100 × 100 × 100 = 1 000 000 cm³ = 1 000 000 mL = 1000 L. -->

<!-- Speaker note: Teacher: ask Ravi to draw his cubic metre. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Find the mistake

**Ravi works out how much a 2 m³ tank holds. Click the line where his working goes wrong.**

```
 1  A water tank holds 2 m³.
 2  1 m = 100 cm, so 1 m³ = 100 cm³.
 3  So the tank holds 2 × 100 = 200 cm³.
 4  That is 200 mL.
```

* Answer: line 2

<!-- Speaker note: Line 2: a cubic metre is 100 cm in each of three directions: 100 × 100 × 100 = 1 000 000 cm³. The tank holds 2000 L. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Choosing units

**Which unit suits the capacity of a backyard swimming pool?**

- Cubic centimetres
- Litres, to the nearest millilitre
- Millilitres
- Kilolitres (or cubic metres)

* Answer: Kilolitres (or cubic metres)

<!-- Speaker note: A pool holds tens of kilolitres (tens of cubic metres). -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Tanks and cartons



- **A tank:** 
- **Litres to cm³:** 
- **Millilitres to cm³:** 
- **Which is a volume?:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/measurement/volume-and-capacity/?full=step-4#step-4)

<!-- Speaker note: What this step is for: Building a tank in metres, converting both ways, and the difference between cm and cm³. Hints, in order: 24 000 L is 24 m³. / Try a base of 4 m by 3 m. For students who need more support: Keep the conversion table visible; use real containers labelled in mL and L. For early finishers: A rainwater tank is 2 m long, 2 m wide and 1.5 m tall. How many days would it supply a family that uses 180 L a day? The hard part, on purpose: Converting cubic units. Ask students to draw a cube and label 100 cm on all three edges before they convert. When students get stuck: A student says 1 m³ = 100 cm³. Ask: How many cm along each of the three edges? Fix: 100 × 100 × 100 = 1 000 000 cm³. / A student mixes up cm and cm³. Ask: Is that a length, an area or a volume? Fix: Cubic units for volume. / A student divides by 100 for mL to L. Ask: How many mL in a litre? Fix: 1000 mL = 1 L. -->

<!-- Speaker note: Teacher: ask which unit a council would use for a dam. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## mL to L

**Write 4500 mL in litres.**

* Answer: 4.5

<!-- Speaker note: 4500 ÷ 1000 = 4.5 L. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## m³ to L

**A container holds 0.6 m³. How many litres is that?**

* Answer: 600

<!-- Speaker note: 0.6 × 1000 = 600 L. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## A box

**A box is 20 cm by 15 cm by 10 cm. How many litres does it hold?**

* Answer: 3

<!-- Speaker note: 20 × 15 × 10 = 3000 cm³ = 3000 mL = 3 L. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Review: triangular prisms

**Review: a triangular prism has a right-triangle end with legs 3 cm and 4 cm, and is 10 cm long. What is its volume in cm³?**

* Answer: 60

<!-- Speaker note: Base area ½ × 3 × 4 = 6 cm², times 10 = 60 cm³. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Make: a juice carton

Then say which of your designs would fit best in a lunch box, and why.

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/measurement/volume-and-capacity/?full=step-6#step-6)

<!-- Speaker note: What this step is for: Designing to a capacity with a constraint uses volume and capacity together. Hints, in order: 600 mL = 600 cm³. / Try a base of 10 cm by 6 cm. -->

<!-- Speaker note: Teacher: ask whose carton is easiest to hold. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Exit ticket

**A fish tank is 50 cm by 30 cm by 40 cm. How many litres does it hold?**

* 50 × 30 × 40 = 60 000 cm³ = 60 L.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this leads: This starts AC9M8M02. Where it leads: prism problems (next lesson), and volume of cylinders (Year 9). -->