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Circumference of a Circle

Circumference of a Circle. Lesson 10.8. Perimeter. the perimeter is the distance around a figure. Find the perimeter to side ratio. 6 units. 6 units. 6 units. 6 units. Find the perimeter to side ratio. Total Perimeter = 6 x 4 or 24 units. Find the perimeter to side ratio. 11 units.

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Circumference of a Circle

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  1. Circumference of a Circle Lesson 10.8

  2. Perimeter • the perimeter is the distance around a figure

  3. Find the perimeter to side ratio 6 units 6 units 6 units 6 units

  4. Find the perimeter to side ratio Total Perimeter = 6 x 4 or 24 units.

  5. Find the perimeter to side ratio 11 units

  6. Find the perimeter to side ratio 3 units

  7. Find the perimeter to side ratio Why is the perimeter/side ratio always 4? A square consists of 4 sides of equal length. Therefore, the perimeter of a square is 4 times the length of one of its sides.

  8. Open Your Math Journals • Complete page 370 with a partner that does not sit at your table. • You will need to take you time to understand what the question is asking. • Read the question 1 carefully. • Study the chart to understand the information it presents. • Answer questions 2 & 3

  9. Now How About Circles? • Today we are going to explore similar ratios for circles. • What is the name for the perimeter of a circle? • circumference • What is the circumference of the Earth?

  10. Circumference Vocabulary Time!!!!! Take out your spiral!

  11. How about a tune?

  12. Add this diagram to your notes radius diameter c i r e c c u m n e f e r

  13. What do you notice? 3 inches 6 inches

  14. What do you notice? 12 inches 24 inches

  15. What do you notice? 1.5 inches 3 inches

  16. What do you notice? 50 inches 100 inches

  17. So, what did you notice? The radius is ½ of the diameter. The diameter is twice the radius.

  18. Is the circumference longer or shorter than the diameter? 1 foot

  19. Is the circumference longer than twice the diameter? 1 foot

  20. Which path is longer-around the square or around the circle? 1 foot

  21. We can conclude that the circumference is more than 2 diameters, but less than 4 diameters. 1 foot

  22. Time to measure! • You and a new partner will complete MJ page 371. • Choose an object from the back table. (It doesn't have to be your object) • Measure the circumference by wrapping the string around the widest part of the circle – make sure the string is straight around the object, not on an angle.

  23. Time to measure! • Carefully remove the string from the object marking the starting and ending point of the circumference. • Measure this length of string in centimeters using your ruler. • Convert to millimeters. (÷10) 27 cm = 2.7 mm • Record the length in millimeters.

  24. Time to measure! • To determine diameter of spheres, place your object on the corner of a piece of computer paper.

  25. Time to measure! • The points where the sides of the angle intersect the circle are the endpoints of the diameter.

  26. Math Journal page 371 • Complete the table • When you record your answers, round to the hundredths place • Answer question 5 • When you complete question 5, come to the board and input your information on the stem and leaf plot • We will be working together to answer question 6

  27. Results • Remember the perimeter/side ratio for a square? • 4 • The circumference/diameter ratio also appears to be a constant with a value of between 3.1and 3.2 • The exact value of this ratio is an irrational number named for a letter of the Greek alphabet –π (pi)

  28. Ratio of a circle circumference = π diameter

  29. Mathematical Pi

  30. I love pi

  31. What is π ? • It is impossible to calculate the exact value of π • In 1949, it was calculated out to 37,000 decimal places on one of the first computers • In 1981 to 2 million digits on a supercomputer • In 1999, there were more than 206 billion digits

  32. What is π ? • Because π goes on forever without a pattern, we use an approximation of its exact value. • Because we approximate the value, our calculations of π cannot be exact. • We will use the symbol ≈ to mean approximately equal to

  33. Let’s Practice • Return to the chart on MJ page 371 • Using the diameter measurement and the value of π, recalculate the circumference of one or two of your objects • Remember your answer will be an estimate and will not be exact.

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