Area of a circle

Using the definition of π \[\pi = \frac{C}{d}=\frac{C}{2r}\]

one can find half of the circumference of a circle \[\frac{C}{2}=r\cdot \pi\]

In the applet above, the rectangle has the width r·π, where r is the radius of the circle, and the height r. Check the check box to see the rectangle. Explain why the area of the circle is: \[A=r^2\cdot \pi\]

Demonstration of Pi

π is defined to be the ratio of the circumference C of a circle to its diameter d \[\pi = \frac{C}{d}=\frac{C}{2r}\]

This ratio is the same for all circles regardless of the size of a circle.