1 Circle Formulae 1 The circumference of a circle Tandi Clausen-May Click the mouse

2 Click the mouse only when you see or If you click too soon you will miss the best bits. Click the mouse Click to see Click the mouse

3 The circumference of a circle Tandi Clausen-May Click the mouse

4 First we need  (pi) Is it… …..? What is  ? Is it a number? Click the mouse

5  Well… not exactly.  is a ratio. Click the mouse

6 Pi is the number of times you must travel straight across the circle to go the same distance as all the way round the circle. Once across twice across So  is a bit more than 3. Click the mouse Click to see the paths three times across and a bit further!

7 How can we be sure that  is a bit more than 3? For a regular hexagon, the distance all the way round is exactly 3 times the distance straight across the middle Click the mouse Click to see the paths

8 And all the way round the circle is a little bit more than all the way round the hexagon. So all the way round the circle is a little bit more than 3 times straight across the middle. Circumference =  × Diameter Click the mouse Click to see the paths

9 Click the mouse Summary Circumference =  × Diameter

10 Circle Formulae 2 The area of a circle Tandi Clausen-May Click the mouse

11 Click the mouse only when you see or If you click too soon you will miss the best bits. Click the mouse Click to see Click the mouse

12 The area of a circle Tandi Clausen-May Click the mouse

13 Click the mouse We saw in Circle Formulae 1 that… Circumference =  × Diameter Now, what about the area?

14 Imagine a circle made out of strands of beads. Open it out. Click the mouse Click to see the circle open

15 circumference radius (half the diameter) Let’s watch that again. It’s a triangle! base = circumference Click to see the circle open again height = radius (half the diameter) Click the mouse

16 circumference radius (half the diameter) = Circumference × Radius 2 Area of the triangle circle Area of the triangle We know how to find the area of a triangle. Click the mouse = Base × Height 2

17 = Circumference × Radius 2 Area Summary Click the mouse

18 Alternatively

19 Area of a Circle Split the circle into 8 equal sectors. Arrange the sectors to resemble a shape that is roughly rectangular. As the sectors get smaller and smaller the resulting shape eventually becomes a rectangle. The area of that rectangle is the same as the area of the circle. ½C rr A A = ½ C x r = ½ x 2 x π x r x r (C = 2 πr) = π x r x r = π r 2

20 The End Tandi Clausen-May