--- title: "Volume and capacity" subtitle: "Area, volume, circles and Pythagoras · Volume · Lesson 14" --- # Volume and capacity **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** 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? :::teacher-note **In one sentence:** Students build boxes and tanks, read their volume and capacity together, and convert between cm³, mL, L and m³ (AC9M8M02, node 1). **Students should be able to say:** 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. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict How many cubic centimetres is it, and how many millilitres is that? :::keep-together **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 My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 1 L. 10 × 10 × 10 = 1000 cm³, and each cm³ holds 1 mL: 1000 mL = 1 L. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Converting units :::keep-together ### Cubic metres **How many litres does 1 m³ hold?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1000 1 m³ = 100 × 100 × 100 = 1 000 000 cm³ = 1 000 000 mL = 1000 L. ::: :::keep-together ### 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. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 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. ::: :::keep-together ### Choosing units **Which unit suits the capacity of a backyard swimming pool?** ☐ Cubic centimetres ☐ Litres, to the nearest millilitre ☐ Millilitres ☐ Kilolitres (or cubic metres) ::: :::teacher-note **Answer:** Kilolitres (or cubic metres) A pool holds tens of kilolitres (tens of cubic metres). ::: :::typical ## Tanks and cartons **A tank.** **Litres to cm³.** **Millilitres to cm³.** **Which is a volume?.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Volume and capacity :::keep-together ### mL to L **Write 4500 mL in litres.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 4.5 4500 ÷ 1000 = 4.5 L. ::: :::keep-together ### m³ to L **A container holds 0.6 m³. How many litres is that?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 600 0.6 × 1000 = 600 L. ::: :::keep-together ### A box **A box is 20 cm by 15 cm by 10 cm. How many litres does it hold?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3 20 × 15 × 10 = 3000 cm³ = 3000 mL = 3 L. ::: :::keep-together ### 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: {{field-15}} ::: :::teacher-note **Answer:** 60 Base area ½ × 3 × 4 = 6 cm², times 10 = 60 cm³. ::: ## Make: a juice carton Then say which of your designs would fit best in a lunch box, and why. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A fish tank is 50 cm by 30 cm by 40 cm. How many litres does it hold?** {{lines-3}} ::: :::teacher-note **Answer:** 50 × 30 × 40 = 60 000 cm³ = 60 L. :::