Circles

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Slide 1: Tekstslide
WiskundeMiddelbare schoolvwoLeerjaar 1

In deze les zitten 17 slides, met interactieve quizzen en tekstslides.

time-iconLesduur is: 50 min

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Slide 1 - Tekstslide

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.

Slide 2 - Tekstslide

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=πr2
C=2πr

Slide 3 - Tekstslide

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

Slide 4 - Tekstslide

If a circle has a radius of 4 what is it's area?
A
4pi
B
8pi
C
12pi
D
16pi

Slide 5 - Quizvraag

If a circle has a radius of 4 what is it's circumference?
A
4pi
B
6pi
C
8pi
D
2pi

Slide 6 - Quizvraag

If a circle has a radius of 6 what is it's area?
A
6pi
B
12pi
C
24pi
D
36pi

Slide 7 - Quizvraag

If a circle has a radius of 6 what is it's circumference?
A
3pi
B
6pi
C
12pi
D
36pi

Slide 8 - Quizvraag

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.

Slide 9 - Tekstslide

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
π42=16π
π62=36π
36π16π=20π

Slide 10 - Tekstslide

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.
A
2pi
B
24pi
C
49pi
D
4pi

Slide 11 - Quizvraag

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.
A
9pi
B
24pi
C
27pi
D
32pi

Slide 12 - Quizvraag

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:



41πr2

Slide 13 - Tekstslide

Calculate the shaded area of the circle with a radius of 6.
A
36pi
B
24pi
C
12pi
D
9pi

Slide 14 - Quizvraag

Calculate the white area of the circle with a radius of 4.
A
16pi
B
12pi
C
8pi
D
4pi

Slide 15 - Quizvraag

Calculate the area of 4 of the pink pieces, if the circle has a radius of 6.
A
9pi
B
12pi
C
15pi
D
18pi

Slide 16 - Quizvraag

Calculate the red part of the circle. The radii are 5 and 7.
A
4pi
B
6pi
C
8pi
D
10pi

Slide 17 - Quizvraag