The document provides information on calculating the circumference and area of circles using the correct formulas. It defines key terms like diameter and radius. It gives examples of using the formulas to find circumference given diameter, diameter given circumference, and area given radius. It also covers the formula for finding the area of an annulus and provides practice problems calculating areas of circles and annuli.

1. Calculate the Circumference Using the Correct Formula 3 Feb 2011 Calculate the circumference and area of a circle and the area of an annulus Level 6 © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk

2. Diameter = 12 cm C = Π d C = 3.14 X 12 C = 37.68 cm How to calculate the circumference © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk The rule to find the circumference is Π x diameter. The value of Π is approximately 3.14 To distance all the way around a circle is called the circumference. Write down the rule. Write down what the rule actually means

3. Diameter = ?cm d = C ÷ Π d = C ÷ 3.14 d = 40 ÷ 3.14 d = 12.73 How to calculate the diameter from the circumference If the circumference is 40 cm. evaluate the DIAMETER © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk

4. Remember d = 2 X r r = d ÷ 2 © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk Diameter Radius Circumference 1 24 2 14 3 17 4 30 5 22 6 120 7 78 8 88 9 120 10 340

5. © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk Diameter Radius Circumference 1 24 12 75.36 2 14 7 43.96 3 34 17 106.76 4 60 30 188.4 5 22 11 69.08 6 120 60 376.8 7 156 78 489.84 8 176 88 552.64 9 38.22 19.11 120 10 108.28 54.14 340

6. The Circle RADIUS The distance from the centre to the edge DIAMETER The distance from one side to the other passing through the centre Π = 3.14 (approximately) D = 2 x R and R = D ÷ 2 © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk

7. Radius = 5 cm Area = Π r 2 A = 3.14 x 5 x 5 A = 78.5 cm 2 How to calculate the area of a circle © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk The rule to find the area is A = Π x r 2 . The value of Π is approximately 3.14 Write down the rule. Write down what the rule actually means

8. 4 cm 3 cm 6 cm A = Π r 2 A = 3.14 x 4 x 4 A = 50.24 cm 2 A = Π r 2 A = 3.14 x 3 x 3 A = 28.26 cm 2 A = Π r 2 A = 3.14 x 6 x 6 A = 113.04 cm 2 10 cm 8 cm 12 cm 314 cm 2 200.96 cm 2 452.16 cm 2 1 . 2. 3. 4 . 5 . 6 . © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk

9. © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk Calculate the areas of the following circles 1 Radius = 10 cm 5 Diameter = 24 cm 2 Radius = 15 cm 6 Diameter = 21 cm 3 Radius = 13.5 cm 7 Diameter = 3.8 cm 4 Radius = 8.75 cm 8 Diameter = 12.5 cm

10. © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk Calculate the areas of the following circles 1 314 cm 2 5 452.16 cm 2 2 706.5 cm 2 6 346.19 cm 2 (2 dp) 3 572.265 cm 2 7 11.34 cm 2 (2 dp) 4 240.41 cm 2 (2 dp) 8 122.66 cm 2 (2 dp)

11. If you know the area and need to calculate the radius the formula is: r = √(A ÷ π ) For example, what is the radius of a circle with an area of 120 cm 2 ? r = √( 120 ÷ 3.14) r = √38.217 r = 6.18 cm to 2 d.p. © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk

12. © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk Calculate the radii of circles with the following areas. 1 314 cm 2 5 452.16 cm 2 2 706.5 cm 2 6 346.19 cm 2 3 572.265 cm 2 7 11.34 cm 2 4 240.41 cm 2 8 122.66 cm 2

13. © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk The radii for the previous question 1 Radius = 10 cm 5 Radius = 12 cm 2 Radius = 15 cm 6 Radius = 10.5 cm 3 Radius = 13.5 cm 7 Radius = 1.9 cm 4 Radius = 8.75 cm 8 Radius = 6.25 cm

14. The area of an ANNULUS R r For this example R = 10 metres and r = 5 metres A = π (R + r)(R – r) A = π (15 +5)(15 – 5) A = 3.14 x 15 x 5 A = 235.5 metres 2 © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk

15. Calculate the area of each annulus described in the table. © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk r R 1. 4 6 2. 3 7 3. 5 15 4. 12 18 5. 4 16 6. 13 19 7. 6.5 13.5

16. © Brain-Cells: E.Resources Ltd. All Rights Reserved www.brain-cells.co.uk r R units 2 1. 4 6 62.8 2. 3 7 125.6 3. 5 15 628 4. 12 18 565.2 5. 4 16 753.6 6. 13 19 602.88 7. 6.5 13.5 439.6