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The circumference and area of a circle

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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,

C= pi d or C = 2 pir

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,

A = pi r squared

Susan Addington, Created with GeoGebra

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Last updated April 13, 2010

Copyright 2009-10 David Dennis and Susan Addington. All rights reserved.