Why is the area of a circle pi times the square of the radius?
usual definition of pi is the ratio of the circumference of a
its diameter, so that the circumference of a circle is pi times
diameter, or 2 pi times the radius. The animation above shows that
circle can be cut and rearranged to closely resemble a
(with height r and base pi times r) of area pi times the square of
radius. By dividing the circle into more than eight slices, the
approximation obtained in this manner would be even better. By
the circle into more and more slices, the approximating
approximate the area of the circle arbitrarily close. This give a
geometric justification that the area of a circle really is "pi r
For another justification for the area of a circle, see The Area of a Circle II.
Last updated, Jan. 29, 2008