Andrew J. Kartsounes
September 18th, 2012
The Circle Lab II
PURPOSE
To create graphical and mathematical representations of the relationship
between the area and the radius of a circle.
APPARATUS
1 cm x 1 cm graph paper
Various circular objects
r
PROCEDURE
1. Trace the circular object onto the graph paper.
2. Count the number of squares and record as the area of the circle.
3. Be sure to estimate partial squares.
4. Measure the diameter of the circle with the graph paper; divide by 2 to calculate
the radius and record.
5. Repeat for all circular objects.
DATA
Radius (cm)
0
2.1
2.8
3.0
4.2
5.1
6.3
7.0
8.0
11.0
Area (cm2)
0
13.9
24.6
28.3
55.4
81.7
124.7
153.9
201.1
380.1
The Circle Lab
page 2
EVALUATION OF DATA
We graphed the area vs. the radius and got a top-opening parabola. The area
vs. the radius2 was then graphed which resulted in a straight line of correlation
coefficient 1.000. Since the relationship is linear and the line contains (0,0), the area
is directly proportional to the radius2.
CONCLUSION
As stated in the EVALUATION OF DATA section, the area (A) is directly
proportional to the radius2 (r2).
A  r2
Since the y-intercept found from the graph is less than 5 % of the maximum
circumference, the y-intercept is negligible. This means that when the radius of a
2
circle is 0 cm, the area is 0 cm2. The slope of the graph is 3.14 cm
.
cm 2
Therefore, our math model is
A  3.14r 2
The Circle Lab
page 3
The slope of the area vs. radius2 graph is defined as pie (  ). Substituting this into
the math model gives us a general math model of
A   r2
A percent error calculation shows that our value of pie is off by 0 %. Any error in this
experiment may have been caused by the difficulty in estimating when using the
graph paper.