Finding the Area of a Circle

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Finding the Area of a Circle
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Take a circle . . .
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Divide it up into sectors
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Colour the top semicircle green the lower
semicircle yellow
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Pull the sectors apart
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Arrange the green sectors in one line the
yellow sectors in another line
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The sectors fit together like teeth . .
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The sectors fit together like teeth . .
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The sectors fit together like teeth . .
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The sectors fit together like teeth . .
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Think about the lengths involved . .
?
?
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The vertical one is easy . . .
r
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Its the radius!
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The other is . . .
r
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Half the circumference
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Remember the formula for the circumference . . .
r
?
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So, half the circumference is . . .
r
?
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So, we have . . .
r
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But this shape is almost a rectangle . . .
r
So can you approximate its area?
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The area is approximately
r
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Now, think . . .
r
What would happen if you cut the circle into
smaller and smaller sectors?
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It would become even more like a rectangle . . .
So this approximation for the area of the circle
would be even more accurate . . .
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So the area of a circle is . . .
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