Presentation on theme: "The Circle Introduction to circles Let’s investigate… Circumference"— Presentation transcript:
1The Circle Introduction to circles Let’s investigate… Circumference Circumference examplesArea of a circleArea examples
2To identify the main parts of a circle. Main part of a CircleLearning IntentionTo identify the main parts of a circle.Success CriteriaKnow the terms circumference, diameter and radius.Identify them on a circle.Calculate the circumference using formula.
3Main part of a Circle Main parts of the circle radius Diameter Circumference
4How can we measure the circumference? Let’s investigate…circumferenceWe can use a ruler to measure the diameter.How can we measure the circumference?
5Let’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.
6circumference ÷ diameter Let’s investigate…Look at the columncircumference ÷ diameter3.14circumference ÷ diameter is roughly
7Let’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!
8If it goes on for ever how can I write it down? The CircumferenceIf it goes on for ever how can I write it down?MathematicalGenius!We use the Greek letterinstead.This is called pi.
9The Circumference Circumference = x diameter C = d So circumference ÷ diameter =By re-arranging this we get:Circumference =x diameterC =d
10The CircumferenceWhen 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 haveThen use 3.14 instead.
11Example 1C = dC = x 66cmC = 18.8cmPressThen x 6 =What is the circumference of this circle?
12Example 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
13There is a much more accurate way! Area of a circle1?234567MathematicalGenius!8To find the area we could try counting the squares inside the circle…There is a much more accurate way!
14There is a special formula for the area of a circle. x radiusA =r²Remember:r² means r x r
15Example 1 A = r² A = x 4 x 4 4m A = 50.3m² Press Then x 4 x4 = What is the area of this circle?
16Example 2 ? A = r² r = ½ x 14 = 7cm 7cm A = x 7 x 7 14cm A = 153.9cm² Don’tforget!r =½ x 14= 7cm7cm?A = x 7 x 714cmA = 153.9cm²PressThen x 7 x 7 =What is the area of this circle?
17Example 3 ? A = r² 24m r = ½ x 24 = 12m 12m A = x 12 x 12 A = 452.4m² Don’tforget!24mr =½ x 24= 12m12m?A = x 12 x 12A = 452.4m²What is the area ofthis semi-circle?Area of semi-circle= ½ x 452.4=226.2m²First work out area of full circle.A semicircle is half a circle.
18Joke 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!