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Finding the Area of a Circle

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

?

Its 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 . . .

So this approximation for the area of the circle

would be even more accurate . . .

So the area of a circle is . . .

(No Transcript)

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