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Investigating Circles

Investigating Circles. Properties of Circles. radius. diameter. Circle A closed curved with all points the same distance from center. •. . origin. area. circumference. Origin. The origin is the center of the circle.

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Investigating Circles

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  1. Investigating Circles

  2. Properties of Circles

  3. radius diameter Circle A closed curved with all points the same distance from center •  origin area circumference

  4. Origin • The origin is the center of the circle. • All points on a circle are the same distance from the origin. • A circle is named by its center. • Name: Circle A origin A

  5. Diameter • The diameter is the distance of a line segment going across a circle through its center. AB • It divides the circle exactly in half. • Is viewed as a line of symmetry. • Symbol islower case d. diameter

  6. Radius • Radius is the distance from the center of the circle to any point on the circle. • Radius is one-half the length of the diameter. • Symbol is lower case r.

  7. Circumference • Circumference refers to the total distance around the outside of a circle. • Can also be called the perimeter of a circle. • Symbol is an upper case C.

  8. Diameter, Radius, Circumference of a Circle

  9. Diameter, Radius, Circumference of a Circle

  10. Making Connections • You can estimate the age of a tree by measuring the circumference of a tree. For many kinds of trees, each 2 cm represents one year of growth. 100 cm

  11. Making Connections • An odometer is an instrument used to measure the distance a vehicle travels by counting the number of wheel revolutions.

  12. Circle Properties • closed curved • all points same distance from centre (origin) • radius • diameter • circumference • area • pi

  13. Origin Diameter Radius Circumference Ratio of C & d center of a circle distance across center of circle (d) half the distance of diameter (r) distance around the outside of a circle ( C ) Circumference is actually 3.14 ( ) bigger than the diameter or about 3 times bigger Concepts you Should Now Know

  14. Diameter, Radius, Circumference of a Circle

  15. Ratio Of The Circumference Of A Circle To Its Diameter • If you measure the distance around a circle (C) and divide it by the distance across the circle through its center (d), you should always come close to a particular value • We use the Greek letter to represent this value.  (pi)

  16. Ratio Of The Circumference Of A Circle To Its Diameter • The value of  is approximately 3.14159265358979323. . . • So, C/d always = ___ • Using is a quicker way to find the circumference of a circle. • Using  allow us to calculate circumference with less measuring,  (pi)

  17. How  Helps 2cm • Knowing the value of ,allows us to use formulas to calculate circumference. • If the diameter of a circle is 2 cm, how could you calculate the circumference? • C =  x ___ • Estimate the circumference • The circumference is ____

  18. Circumference of a Circle  • C = x d • C = 3.14 x 3 • C = 9.42cm If the diameter is 3cm

  19. Circumference of a Circle Estimate Is . . .  • C = x d • C = 3.14 x 1.5 • C = 4.71cm If the diameter is 1.5cm

  20. Circumference of a Circle C =  x d …but we don’t know the diameter  • C = x d • d = 2 x r • d = 2 x 3 • d = 6 • C = 3.14 x 6 • C = 18.84m If the radius is 3m

  21. Circumference of a Circle  • C = x d • C = 3.14 x 5 • C = 15.7 Estimate is . . If the diameter is 5

  22. Diameter of a Circle What formula could I use? What is the diameter of a circle if the circumference is 18.8?

  23. Diameter of a Circle What is the diameter of a circle if the circumference is 13.2?

  24. Diameter of a Circle What is the diameter of a circle if the circumference is 33.9?

  25. Area of a Circle

  26. Area of a Circle Estimate the area of this circle.

  27. Area of a Circle Seeing the square units can help. Remember each block is one square unit Estimate is

  28. Area of a Circle Counting square units can give you a good estimate, however, can be time consuming. Counting will not always give an exact answer. Actual is The formula for finding the area of a circle is A =  x r x r or  r2 Estimate is

  29. Area of a Circle Estimated area is Remember A =  x r x r or  r2 Actual area is

  30. Area of a Circle Estimated area is Actual area is

  31. Choosing a Formula • To cut across a circular park has a you would travel 0.8 of a kilometer. How far would you travel around the park? • A spoke of a bicycle wheel is 12 cm. What will be the distance of one turn of the wheel?

  32. Other skills FOIL (2x – 5)(3x +6) First Outside Inside Last Collect Like Terms

  33. Multiplying Binomials (2x – 6)(x + 7)

  34. Other SkillsFactoring 2x² + 14x + 12 Find a. b. c. Multiply a x c Find two numbers that add to b ( )( ) x in each Divide by a Kickback

  35. Factoring 3x² + 12x + 12

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