THE AREA OF A CIRCLE

Edwina R. Justice              Gunsaulus Scholastic Academy
                               4420 South Sacramento Ave.
                               Chicago IL   60632
                               (312) 535-7215

OBJECTIVE:
    To see the relationship between circumference and diameter and how that 
relationship, called pi, is used in the formula for the area of a circle. 

MATERIALS:
    A.Round container lids with varying circumferences
    B.Metric tape measures
    C.One graph for wall (label horizontal axis as DIAMETER and vertical
      axis as CIRCUMFERENCE)
    D.One chart with four columns for wall (label CIRCUMFERENCE, DIAMETER,
      C/D, and Lid #)
    E.Graphics
      1.Small square inscribed in a circle inscribed in a larger square
      2.Small hexagon inscribed in a circle inscribed in a larger hexagon
      3.Circle cut into 16 equal pie-shaped pieces and arranged to form 
        a parallelogram
 
STRATEGIES:
    A.Assign group activities
      1.Make a chart, on paper, similar to the wall chart.
      2.Measure C and D to nearest mm.
      3.Calculate C/D and record information on group chart.
      4.Plot points on large wall graph.
      5.Record information on large wall chart. 
      6.Calculate group average for C/D.
    B.Discuss results on graph. Points appear to lie on a straight line.
    C.Establish C/D = pi and C = pi(D)
    D.Review other area formulas:
      1.Area of square = s**2
      2.Area of rectangle = bh
      3.Area of parallelogram = bh
      4.Area of triangle = 1/2 (bh)
    E.Compare apparent area of small square inscribed in a circle with
      apparent area of larger square circumscribed about circle with
      apparent area of circle:    
        Area of sm. sq. (2*r**2) < Area of circle < Area of lge. sq.
        (4*r**2)
    F.Compare areas of small and large hexagons, one inscribed in the 
      circle, the other circumscribed about the circle. Relate to apparent
      area of circle. Discuss how an increase in the number of sides of
      the inscribed and circumscribed figures approaches the shape and 
      area of the circle.
    G.Show how the area of the parallelogram, made from 16 pieces of the
      circle is equal to pi(r**2):
              A = bh
                = 1/2 (C) (r)
                = 1/2 (pi*2r) (r)
                = pi (r) (r)
                = pi (r**2)

    H.Discuss values on wall chart. Calculate average. Compare average
      with actual value of pi.
    I.Calculate area of circle using pi formula. Relate to figures in
      graphics.

Also see the file guests/edwina1.html