The circumference and area of a circle
Click, then unclick, the checkboxes to show:
Circumference measurement:
- The circumference of a circle, rolled out along a number line. Roll the circle with the slider, or use the triangular "play" button in the lower left of the window.
- The rolled out circumference measured with radii of the circle, and with diameters of the circle
Conclusion: the circumference of a circle is pi diameters, or 2 pi radii of the circle. As formulas,
Area measurement:
- The circle, subdivided into increasing numbers of sectors; use the slider to change the number of subdivisions
- The same subdivisions, arranged to make a parallelogram-like shape
- A rectangle with the same area as the rearranged circle, measured with pi squares, r units on a side.
Conclusion: the area of a circle is pi r squares, As a formula,
Susan Addington, Created with GeoGebra |
