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Finding the Area of a Circle

Finding the Area of a Circle . Take a circle . . . Divide it up into sectors. Colour the top semicircle green & the lower semicircle yellow. Pull the sectors apart. Arrange the green sectors in one line & the yellow sectors in another line. The sectors fit together like teeth . . .

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Finding the Area of a Circle

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  1. Finding the Area of a Circle

  2. Take a circle . . .

  3. Divide it up into sectors

  4. Colour the top semicircle green & the lower semicircle yellow

  5. Pull the sectors apart

  6. Arrange the green sectors in one line& the yellow sectors in another line

  7. The sectors fit together like teeth . .

  8. The sectors fit together like teeth . .

  9. The sectors fit together like teeth . .

  10. The sectors fit together like teeth . .

  11. Think about the lengths involved . . ? ?

  12. The “vertical” one is easy . . . r ? It’s the radius!

  13. The other is . . . r ? Half the circumference

  14. Remember the formula for the circumference . . . r ?

  15. So, half the circumference is . . . r ?

  16. So, we have . . . r

  17. But this shape is almost a rectangle . . . r So can you approximate its area?

  18. The area is approximately r

  19. Now, think . . . r What would happen if you cut the circle into smaller and smaller sectors?

  20. r It would become even more like a rectangle . . . So this approximation for the area of the circle would be even more accurate . . .

  21. So the area of a circle is . . .

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