Finding the Area of a Circle
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Finding the Area of a Circle PowerPoint PPT Presentation


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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 . . .

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Finding the Area of a Circle

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Finding the area of a circle

Finding the Area of a Circle


Take a circle

Take a circle . . .


Divide it up into sectors

Divide it up into sectors


Colour the top semicircle green the lower semicircle yellow

Colour the top semicircle green & the lower semicircle yellow


Pull the sectors apart

Pull the sectors apart


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

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 teeth1

The sectors fit together like teeth . .


The sectors fit together like teeth2

The sectors fit together like teeth . .


The sectors fit together like teeth3

The sectors fit together like teeth . .


Think about the lengths involved

Think about the lengths involved . .

?

?


The vertical one is easy

The “vertical” one is easy . . .

r

?

It’s the radius!


The other is

The other is . . .

r

?

Half the circumference


Finding the area of a circle

Remember the formula for the circumference . . .

r

?


Finding the area of a circle

So, half the circumference is . . .

r

?


Finding the area of a circle

So, we have . . .

r


Finding the area of a circle

But this shape is almost a rectangle . . .

r

So can you approximate its area?


Finding the area of a circle

The area is approximately

r


Finding the area of a circle

Now, think . . .

r

What would happen if you cut the circle into smaller and smaller sectors?


Finding the area of a circle

r

It would become even more like a rectangle . . .

So this approximation for the area of the circle would be even more accurate . . .


Finding the area of a circle

So the area of a circle is . . .


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