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The Circle Introduction to circles Let’s investigate… Circumference

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Presentation on theme: "The Circle Introduction to circles Let’s investigate… Circumference"— Presentation transcript:

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

2 To identify the main parts of a circle.
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 Main part of a Circle Main parts of the circle radius Diameter
Circumference

4 How can we measure the circumference?
Let’s investigate… circumference 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 circumference ÷ diameter
Let’s investigate… Look at the column circumference ÷ diameter 3.14 circumference ÷ diameter is roughly

7 Let’s investigate… circumference ÷ diameter is roughly 3.14
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. We’ll stop here since it would stretch for 600 miles if we printed them all!

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

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

10 The Circumference When doing circle calculations, you will normally use a calculator. Some calculators have a button like this: 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.

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

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

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

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

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

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

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