§8.5 Area of a circle

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

§8.5 

Learning goal:

How to calculate the area of a circle

So today: the AREA of a CIRCLE

Recap on last lesson:     Circumference (omtrek) circle =        x d

For example:

If radius = 3, then

you can calculate the 

Circumference as here:

π

Suppose we want 

to calculate the AREA of this circle.

There's a fine way of going about it!

step 1:   we slice up the circle in 15 equal parts.

step 2:  the equal parts are placed so that they form 

                a kind of a rectangle

step 3:  the 'rectangle' is clearly improved!

                 now the 2 shorter sides are vertical straight lines,

                 but the 2 longer sides are not quite straight lines,

                 because they consist of a series of arcs.

   The 2 longer sides are not quite straight lines,

    because they consist of a series of arcs.                        

    Another improvement would be:

    slicing up the parts in many more equal parts.

    In this way the 'rectangle' would get better all the time!

    Anyway, this would be very interesting, but we WON'T DO it.

Now be ready for an exercise in your Notebook:

- open your Notebook

- take before you a pen

- prepare yourself for an interesting task, that will lead up to:

   The Formula for the AREA of a CIRCLE!       

2 remarks:

1st     Answer this task in your Notebook.

2nd  Give your answer in an exact form ( .... x     )  and also as an

          approximation.

π

Solution:

       x  10                  31.4 

So when      is taken as 3.14 then the rounded off outcome

equals 31.4                  Of  course this is not very precise.

By the way, did you know about Jim the Circle?

π

≈

π

- Make this task in your Notebook.

- Give your answer in an exact form and also rounded off, again.

- Key in both answers in the next slide!

30b How long is AB measured along the arcs?

Solution:

Length AB is half of the circumference of the circle.

So AB = 5 x 

Rounded:     31.4 : 2 = 15.7 cm

π

- Make task 30c in your Notebook

- Give your answer in an exact form and also rounded off, again.

Solution:  

This is the most important question of this lesson, because with this formula

we can calculate the Area of each Circle!

Use the formula for a rectangle:   Area = length x width

Solution:

A few practice tasks follow now.

First however once more the formula is shown.

-   Calculate it  exactly, so with       in the answer.

-   Answer the question in the next slide.

π

area pond with radius of 6 is ....

1. pi x 6
2. p x 6 squared
3. pi x 36
4. pi x 36 squared

Solution: as you can read below, both answer B    

                                                                    and answer C.   

                                                                    are good!

π⋅6​2​​

π⋅36

-   Calculate the area exactly again.

-   Key in your answer in the next slide.

The area of a circle with a diameter of 26 is .....

1. 26 squared pi
2. 26 pi
3. 169 pi
4. pi x 13 squared

Solution:

Homework

choose between:

-  31 t/m 35  and

-  33, 34, 35, C9 and C10