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Introduction to circles

The Circle. Introduction to circles. Let’s investigate… Circumference. Circumference examples. Area of a circle. Area examples. Main part of a Circle. Learning Intention To identify the main parts of a circle. Success Criteria Know the terms circumference, diameter and radius.

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Introduction to circles

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  1. The Circle Introduction to circles Let’s investigate… Circumference Circumference examples Area of a circle Area examples

  2. Main part of a Circle Learning Intention To identify the main parts of a circle. • Success Criteria • Know the terms circumference, diameter and radius. • Identify them on a circle. • Calculate the circumference using formula.

  3. radius Diameter Circumference Main part of a Circle Main parts of the circle O

  4. circumference Let’s investigate… We can use a ruler to measure the diameter. How can we measure the circumference?

  5. Let’s investigate…Work as a team at your table • Cut a piece of yarn that is exactly the length of the distance around the circular object at your table. (Called the circumference) • Cut another piece of yarn that is exactly the length of the distance through the middle of your circular object. (Called the diameter) • Use a ruler (in cm) to measure these two pieces of string. Be as accurate as possible! • Use a calculator to divide the Circumference by the diameter.

  6. Let’s investigate… 3.14 Look at the column circumference ÷ diameter circumference ÷ diameter is roughly

  7. 3.14 Let’s investigate… circumference ÷ diameter is roughly There isn’t an exact answer for this. It actually goes on forever! In 1989 a computer worked it out to 480 million decimal places. 3.141592653589793238462643383279502… We’ll stop here since it would stretch for 600 miles if we printed them all!

  8. We use the Greek letter instead. The Circumference If it goes on for ever how can I write it down? Mathematical Genius! This is called pi.

  9. The Circumference So circumference ÷ diameter = 3.1415926535 By re-arranging this we get: x diameter Circumference = d C =

  10. When doing circle calculations, you will normally use a calculator. This button stores to 8 or 9 decimal places which is more than accurate enough! If your calculator doesn’t have Then use 3.14 instead. The Circumference Some calculators have a button like this: 3.141592654

  11. C = d C = x 6 Press Then x 6 = Example 1 6cm C = 18.8cm What is the circumference of this circle?

  12. C = d C = x 10 Example 2 d = 2 x 5 = 10cm 10cm C = 31.4cm 5cm What is the circumference of this circle? Remember: diameter = 2 x radius

  13. ? ? ? ? ? ? 6 7 8 5 1 2 3 4 ? ? Area of a circle Mathematical Genius! To find the area we could try counting the squares inside the circle… There is a much more accurate way!

  14. x radius x radius Area = r² A = Area of a circle There is a special formula for the area of a circle. Remember: r² means r x r

  15. A = r² A = x 4 x 4 Press Then x 4 x4 = Example 1 4m A = 50.3m² What is the area of this circle?

  16. A = r² A = x 7 x 7 Press Then x 7 x 7 = Example 2 Don’t forget! r = ½ x 14 = 7cm 7cm ? A = 153.9cm² 14cm What is the area of this circle?

  17. A = r² A = x 12 x 12 24m Example 3 Don’t forget! r = ½ x 24 = 12m ? 12m A = 452.4m² What is the area of this semi-circle? Area of semi-circle = ½ x 452.4 =226.2m² A semicircle is half a circle. First work out area of full circle.

  18. Joke of the Day! What do you get when you take the circumference of an apple and divide it by the diameter of the apple? Apple Pi!

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