Introduction to circles

Area examples

Let’s investigate… Circumference

Circumference examples

Area of a circle

The CircleThe Circle

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Main part of a CircleMain part of a Circle

Learning IntentionLearning IntentionTo identify the main parts of a circle.To identify the main parts of a circle.

Success CriteriaSuccess Criteria

1.1. Know the terms circumference, Know the terms circumference, diameter and radius.diameter and radius.

2.2. Identify them on a circle.Identify them on a circle.3.3. Calculate the circumference using Calculate the circumference using

formula.formula.

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Main part of a CircleMain part of a Circle

radius

O

Circumference Diameter2D r

12

r D

C D

Let’s investigate…

We can use a ruler to measure the diameter.

How can we measure the circumference?

Let’s investigate…Let’s investigate…Work as a team at your tableWork as a team at your table

1.1. Cut a piece of yarn that is exactly the length of the Cut a piece of yarn that is exactly the length of the distance around the circular object distance around the circular object at your table. at your table. (Called the circumference)(Called the circumference)

2.2. Cut another piece of yarn that is exactly the length of Cut another piece of yarn that is exactly the length of the the distance through the middle of your circular distance through the middle of your circular objectobject. (Called the diameter) . (Called the diameter)

3.3. Use a ruler (in cm) to measure these two pieces of Use a ruler (in cm) to measure these two pieces of string. Be as accurate as possible!string. Be as accurate as possible!

4.4. Use a calculator to divide the Circumference by the Use a calculator to divide the Circumference by the diameter.diameter.

Let’s investigate…Let’s investigate…

Look at the column circumference ÷ diameter

circumference ÷ diameter is roughly 3.14

Circumference Diameter C/d#DIV/0!#DIV/0!#DIV/0!#DIV/0!#DIV/0!#DIV/0!

3.141592653589793238462643383279502…

Let’s investigate…

circumference ÷ diameter is roughly

There isn’t an exact answer for this. It actually goes on forever!

We’ll stop here since it would stretch for 600

miles if we printed them all!

In 1989 a computer worked it out to 480 million decimal places.

3.14

The CircumferenceIf it goes on for ever

how can I write it down?

We use the Greek letter

instead.

MathematicalGenius!

This is called pi.

3.1415926535So circumference ÷ diameter =

Circumference =

x diameter

By re-arranging this we get:

C =

d

The Circumference

This button stores to 8 or 9 decimal places which is more than accurate enough!

3.141592654

When doing circle calculations, you will normally use a calculator.

Some calculators have a button like this:

If your calculator doesn’t haveThen use 3.14 instead.

The Circumference

Example 1

6cm

What is the circumference of this circle?

C = dC = x 6

Press

Then x 6 =

C = 18.8cm

Example 2

5cm

What is the circumference of this circle?

C = d

C = x 10

Remember: diameter = 2 x

radius

C = 31.4cm

d = 2 x 5 = 10cm

10cm

Area of a circle

To find the area we could try counting the squares inside the circle…

1

2 3 4

5 6 7

8

?

?

? ?

? ?

?

?

There is a much more accurate

way!

MathematicalGenius!

Area of a circle

A = r²

Area =

x radius

x radius

There is a special formula for the area of a circle.

Remember:r² means r x r

Example 1

What is the area of this circle?

A = r²A = x 4 x 4

Press

Then x 4 x4 =

A = 50.3m²4m

Example 2

What is the area of this circle?

A = r²

A = x 7 x 7

Press

Then x 7 x 7 =

A = 153.9cm²14cm

?7cm

r = ½ x 14 = 7cm Don’tforget!

24m

Example 3

What is the area of this semi-circle?

A = r²

A = x 12 x 12

A semicircle is half a circle.

A = 452.4m²

?12m

r = ½ x 24 = 12m Don’tforget!

Area of semi-circle

= ½ x 452.4

First work out area of full

circle.

=226.2m²

Joke of the Day!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!