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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