--- title: "Prisms and capacity" subtitle: "Area, volume, circles and Pythagoras · Volume · Lesson 5" --- # Prisms and capacity **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** A tent, a chocolate bar in a triangular box, a drink carton: how much do they hold? If the shape is the same all the way through, one rule finds them all. :::teacher-note **In one sentence:** Students build triangular prisms in layers, find volume as cross-section area × length for any right prism, and link volume to capacity (1 cm³ = 1 mL, 1000 cm³ = 1 L) (AC9M7M02, node 2). **Students should be able to say:** I can find the cross-section of a prism. I can find the volume of a triangular prism. I can change between cm³, mL and litres. **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 What is the area of the triangle end? :::keep-together **A prism's triangle end is half of a 4 cm by 3 cm rectangle. The prism is 5 cm long. What is its volume?** ☐ 60 cm³ ☐ 12 cm³ ☐ 30 cm³ ☐ 6 cm³ My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 30 cm³. The triangle is ½ × 4 × 3 = 6 cm², and 5 layers of 6 is 30. 60 is the whole box; 6 is one layer. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## Cross-section times length :::keep-together ### Any prism Here is the rule for any prism, and capacity. 1. $A = \tfrac{1}{2} \times 6 \times 4 = 12 \text{ cm}^2$ — Find the area of the cross-section (a triangle: halve). 2. $V = 12 \times 10 = 120 \text{ cm}^3$ — Times the length: one layer of 12 for each centimetre. 3. $120 \text{ cm}^3 = 120 \text{ mL}$ — Capacity: 1 cm³ holds 1 mL. 4. $1000 \text{ cm}^3 = 1 \text{ L}$ — 1000 mL is a litre: a 10 cm cube holds 1 L. Now try one: a triangle end with base 6 cm and height 4 cm, 10 cm long. **A prism's cross-section is a triangle with base 6 cm and height 4 cm. The prism is 10 cm long. What is its volume, in cm³?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 120 ½ × 6 × 4 = 12 cm², × 10 = 120 cm³. ::: :::keep-together ### Find the mistake **Lena finds how much air is inside a tent. Click the line where her working goes wrong.** ``` 1 A tent is a triangular prism 3 m long. Its triangle end has base 2 m and height 1.5 m. 2 Area of the triangle end = 2 × 1.5 = 3 m² 3 Volume = 3 × 3 4 = 9 m³ ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: the end is a triangle, so halve: ½ × 2 × 1.5 = 1.5 m². Volume = 1.5 × 3 = 4.5 m³. ::: :::keep-together ### The cross-section **How do you find a prism's cross-section?** ☐ It is the biggest face ☐ It is always the face it stands on ☐ It is the face that is the same shape all the way along, like a slice of bread ::: :::teacher-note **Answer:** It is the face that is the same shape all the way along, like a slice of bread Cut straight across anywhere: the cross-section is what every slice looks like. ::: :::typical ## One change at a time **One litre.** Each task changes one thing. **Litres.** **Millilitres.** **A parallelogram.** **Turned over.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Prisms :::keep-together ### Cross-section given **A prism's cross-section has area 15 cm² and the prism is 8 cm long. Volume, in cm³?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 120 15 × 8 = 120 cm³. ::: :::keep-together ### Litres to cm³ **How many cm³ is 3 litres?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 3000 3 × 1000 = 3000 cm³. ::: :::keep-together ### A tent **A tent's triangle end has base 3 m and height 2 m. It is 4 m long. Volume, in m³?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 12 3 m² × 4 = 12 m³. ::: :::keep-together ### Review: units **Review: write 250 cm in metres.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 2.5 250 ÷ 100 = 2.5 m. ::: ## Make: a 24 cm³ wedge Then find one that is as long as possible. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A prism's triangle end has base 5 cm and height 4 cm; it is 6 cm long. Find its volume and its capacity in mL.** {{lines-3}} ::: :::teacher-note **Answer:** ½ × 5 × 4 = 10 cm², × 6 = 60 cm³ = 60 mL. :::