Take a circle... Divide it up into sectors Colour the top semicircle green & the lower semicircle yellow.

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Presentation transcript:

Take a circle...

Divide it up into sectors

Colour the top semicircle green & the lower semicircle yellow

Pull the sectors apart

Arrange the green sectors in one line & the yellow sectors in another line

The sectors fit together like teeth..

Think about the lengths involved.. ? ?

The “vertical” one is easy... r ? It’s the radius!

The other is... r ? Half the circumference

Remember the formula for the circumference... r ?

So, half the circumference is... r ?

So, we have... r

But this shape is almost a rectangle... r So can you approximate its area?

The area is approximately r

Now, think... r What would happen if you cut the circle into smaller and smaller sectors?

It would become even more like a rectangle... r So this approximation for the area of the circle would be even more accurate...

So the area of a circle is...