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 . .

The sectors fit together like teeth . .

The sectors fit together like teeth . .

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

?

Circumference 2 r

So, half the circumference is . . .

r

?

2

2

rr

So, we have . . .

r

r

But this shape is almost a rectangle . . .

r

r

So can you approximate its area?

The area is approximately

r

r

2Area r r

r

Now, think . . .

r

rWhat would happen if you cut the circle

into smaller and smaller sectors?

It would become even more like a rectangle . . .

r

rSo this approximation for the

area of the circle would be even more accurate . . .

So the area of a circle is . . .

2r