--- title: "Parts of a circle" subtitle: "Area, volume, circles and Pythagoras · Circles · Lesson 6" --- # Parts of a circle **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** Wheels, plates, clocks and pizza: why does a wheel roll smoothly? Because every point on its edge is the same distance from the axle. :::teacher-note **In one sentence:** Students name the parts of a circle (centre, radius, diameter, chord, circumference), use d = 2r in both directions, and reason about the biggest circle that fits a rectangle (AC9M7M03, node 1). **Students should be able to say:** I can name the parts of a circle. I can find the diameter from the radius, and the radius from the diameter. I can explain why the diameter is the longest chord. **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 Picture a radius, then another one pointing the opposite way. :::keep-together **A circle has radius 5 cm. What is its diameter?** ☐ 2.5 cm ☐ 5 cm ☐ 10 cm ☐ 25 cm My prediction, and why: {{lines-3}} ::: :::teacher-note **What happens:** 10 cm: the diameter goes from the edge, through the centre, to the other edge: two radii. 2.5 halves the radius. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## The parts :::keep-together ### Two radii make a diameter Here are the relationships. 1. $d = 2r$ — The diameter is two radii, end to end through the centre. 2. $r = 5 \Rightarrow d = 2 \times 5 = 10$ — Radius to diameter: double. 3. $d = 120 \Rightarrow r = 120 \div 2 = 60$ — Diameter to radius: halve. 4. $C$ — The circumference is the distance round; the next lessons find it from d. Now match the parts. **Match each part of a circle to what it is.** A. right across, through the centre B. the distance all the way round C. a straight line joining two points on the circle D. from the centre to the edge {{columns 60% 40%}} {{rows 1}} | Part | Letter | |---|---| | `radius` | | | `diameter` | | | `chord` | | | `circumference` | | ::: :::teacher-note **Answer:** radius → D. from the centre to the edge; diameter → A. right across, through the centre; chord → C. a straight line joining two points on the circle; circumference → B. the distance all the way round The radius is half the diameter; the diameter is the longest chord; the circumference is the perimeter. ::: :::keep-together ### Find the mistake **Jay works out how far a chair at the edge of a round table is from its centre. Click the line where he goes wrong.** ``` 1 A round table is 120 cm across, measured through the centre. 2 The distance across through the centre is the radius. 3 So the radius is 120 cm. 4 A chair at the edge is 120 cm from the centre. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** line 2 Line 2: across through the centre is the diameter. The radius is half of it: 120 ÷ 2 = 60 cm. ::: :::keep-together ### Chords **Is every chord a diameter?** ☐ Yes: they both go across the circle ☐ No: only a chord that passes through the centre is a diameter ☐ No: a chord is always curved ::: :::teacher-note **Answer:** No: only a chord that passes through the centre is a diameter Every diameter is a chord (the longest one), but most chords miss the centre. ::: :::typical ## One change at a time **Diameter 7.** Each task changes one thing. **Diameter to radius.** **Radius to diameter.** **Opposite radii.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Circle parts :::keep-together ### Double **A clock face has radius 12 cm. What is its diameter, in cm?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 24 2 × 12 = 24 cm. ::: :::keep-together ### Halve **A coin has diameter 3 cm. What is its radius, in cm?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 1.5 3 ÷ 2 = 1.5 cm. ::: :::keep-together ### Longest chord **What is the longest chord of a circle?** ☐ A radius ☐ A diameter ☐ The circumference ☐ Any chord near the edge ::: :::teacher-note **Answer:** A diameter A chord through the centre, the diameter, is the longest. ::: :::keep-together ### Review: volume **Review: a box is 2 cm by 3 cm by 4 cm. What is its volume, in cm³?** Answer: {{field-15}} ::: :::teacher-note **Answer:** 24 2 × 3 × 4 = 24 cm³. ::: ## Make: the biggest circle in a box Then: how many of those circles fit side by side in the lid? Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **A circular pond has diameter 9 m. Find its radius. What is a chord?** {{lines-3}} ::: :::teacher-note **Answer:** 4.5 m. A straight line joining two points on the circle. :::