Why is the area of a circle pi r^2?

1 Answer
George C.
Jan 1, 2016

See explanation...

Explanation:

The circumference of a circle of radius r is of length 2pi r, by the definition of pi.

If you dissect a circular disc into segments of equal size, you can reassemble them head to tail into a sort of bumpy parallelogram with height approximately r and base width approximately pi r, being half of the circumference of the circle. Hence the area is pi r^2.

It works better the smaller your segments are, but here's an animation I made for 8 segments:

enter image source here

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