# The Area of a Circle II Why is the area of a circle pi times the square of the radius? The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pi times the radius. The animation above shows that a circle can be divided into concentric rings which can be unrolled to closely resemble a triangle (with height r and base 2 pi times r) of area pi times the square of the radius.  By dividing the circle into more rings and unrolling, the result more closely matches a triangle, so the approximation becomes better.  Taking more and more rings, the triangle of area "pi r squared" approximates the area of the circle arbitrarily close.   This gives a geometrc justification that the area of a circle really is "pi r squared".

For another justification for the area of a circle, see The Area of a Circle.

### Other Animated Sites

The Area of a Circle
The Pythagorean Theorem
The Sine Curve
The Cosine Curve

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Last updated, Jan. 29, 2008
Tom.Richmond@WKU.edu