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Area of a Circle

Area of a Circle. π. d. d. d. Starter. Which of these shapes has the greatest perimeter? Which has the smallest? What is each perimeter in terms of d ?. d. d. d. ½d. ½d. Starter Answer. Square has 4 sides of length d 4d Hexagon has 6 sides of ½d 3d .

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Area of a Circle

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  1. Area of a Circle π

  2. d d d Starter • Which of these shapes has the greatest perimeter? Which has the smallest? • What is each perimeter in terms of d?

  3. d d d ½d ½d Starter Answer • Square has 4 sides of length d 4d • Hexagon has 6 sides of ½d 3d

  4. Starter Answer • Square has 4 sides of length d 4d • Hexagon has 6 sides of ½d 3d • Circle is between 3d and 4d πd

  5. r r r Areas • Which of these shapes has the greatest area? Which has the smallest? • What is the area in terms of r?

  6. r 2r r r Areas • Large square is 2r x 2r = 4r2 • Small square is half of this = 2r2

  7. Areas • Large square is 2r x 2r = 4r2 • Small square is half of this = 2r2 • Circle has area in between 2r2 and 4r2

  8. Area of a circle • A circle has radius r

  9. Rearrange the sectors

  10. Consider the lengths So the length of this side is πr Circumference of circle = 2πr Length of half circumference = πr

  11. Consider the lengths So the height is r πr Radius of circle = r

  12. Consider the area r πr Area of shape is close to area of parallelogram = base x height = πr x r = πr2 Hence the area of a circle is = πr2

  13. r d Summary • A circle has radius rand diameter d • Circumference of a circle C = πd or C = 2πr • Area of a circle A = πr2 Fiddle-dee-dum, fiddle-dee-dee A ring round the moon is π times d But if you want a hole repaired Then what you need is πr2.

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