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Area of a Circle - The Pizza Method

Area of a Circle - The Pizza Method

The formula for the area of a circle is easy to derive if you use the "pizza method".

A circle is a famous shape, because the ratio of its two most obvious features, the circumference and the diameter, is the same for all circles and is the famous number pi.


The decimal places go on forever.

So, given the diameter of a circle we can easily calculate its circumference.


But what about the area? We can get this by the following clever method..

Just imagine the circle of radius r is a pizza and we cut it into an even number of slices, 2*n where n is an integer. Now take two slices and place them on the table, but position them in opposite directions so they make an approximate rectangle. The length of this rectangle is r and its width is equal to the width of a slice. Of course it's not a perfect rectangle because the top and bottom edges are curvey, but to a good approximation we can say..

area of one rectangle=r*(width of a slice)

But approximately..

width of a slice=circumference/(2*n)=(2*pi*r)/(2*n)=pi*r/n

So, area of one rectangle=r*(width of a slice)=pi*r^2/n

Now, as we increase n the pizza gets cut into thinner and thinner slices and these approximations get better and better. In fact, when n becomes a truly massive number we can call these approximation exact, and so..

area of all the rectangles=n*(area of one rectangle)=pi*r^2

This area must be the same as the circle, so we have..

area of circle=pi*r^2

Which is the correct formula for the area of a circle.

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Content written and posted by Ken Abbott
Internet Marketing Consultant