Circles

• Wiskunde
• Middelbare school
• vwo
• Leerjaar 1

The circle

The circle has a couple of properties that we use:

• It has a midpoint usally called M.
  
• The line that starts in M and goes to the edge of the circle in a straight line is called the radius.
• A straight line that goes from one edge of the circle towards the other edge of the circle is called the diameter.
  

The circle

As with other 2D-shapes we want to calculate area and perimeter of the circle.  The perimeter of a circle is called the circumference. In the formulas below A stands for area, C stands for circumference and r is the radius.


 

A=πr​2​​

C=2πr

PI

An interesting number that is involved with circles is the number pi. In mathematics we use:


This number is calculated when you divide the circumference of a circle by it's diameter.
When we round off pi we get 3.14.

π

If a circle has a radius of 4 what is it's area?

1. 4pi
2. 8pi
3. 12pi
4. 16pi

If a circle has a radius of 4 what is it's circumference?

1. 4pi
2. 6pi
3. 8pi
4. 2pi

If a circle has a radius of 6 what is it's area?

1. 6pi
2. 12pi
3. 24pi
4. 36pi

If a circle has a radius of 6 what is it's circumference?

1. 3pi
2. 6pi
3. 12pi
4. 36pi

Calculating areas

Sometimes we want to calculate only a specific area of a circle.
In the blue circle on the right you see a white circle in the middle.
We can calculate the area of the blue part,
by calculating the area of the big circle first
and then subtracting the area of the white
circle from it.

Calculating areas

Let's say the white circle in the middle has a radius of 4.
And the big circle (including the blue part) has a radius of 6.
The area of the white circle is
The area of the big circle is

The blue area then is

π⋅4​2​​=16π

π⋅6​2​​=36π

36π−16π=20π

Calculate the blue part of the circle, when the radius of the small circle is 5 and the radius of the big circle is 7.

1. 2pi
2. 24pi
3. 49pi
4. 4pi

Calculate the blue part of the circle, when the radius of the small circle is 3 and the radius of the big circle is 6.

1. 9pi
2. 24pi
3. 27pi
4. 32pi

Area of a circle

We can also calculate a part of the area of a circle.
If you know that part is a fraction like 1/2 or 1/3 or 1/4, you just multiply the fraction with the total area.

To calculate the area of the circle to the right:

​4​​1​​⋅π⋅r​2​​

Calculate the shaded area of the circle with a radius of 6.

1. 36pi
2. 24pi
3. 12pi
4. 9pi

Calculate the white area of the circle with a radius of 4.

1. 16pi
2. 12pi
3. 8pi
4. 4pi

Calculate the area of 4 of the pink pieces, if the circle has a radius of 6.

1. 9pi
2. 12pi
3. 15pi
4. 18pi

Calculate the red part of the circle. The radii are 5 and 7.

1. 4pi
2. 6pi
3. 8pi
4. 10pi