Determining the Ratio of the Circumference to the Diameter of

Determining the Ratio of Circumference to Diameter of a Circle

In determining the ratio of the circumference to the diameter I began by
measuring the diameter of one of the si objects which contained circles, then
using a string, I wrapped the string around the circle and compared the length
of the string, which measured the circumference, to a meter stick. With this
method I measured all of the six circles. After I had this data, I went back and
rechecked the circumference with a tape measure, which allowed me to make
a more accurate measure of the objects circumferences by taking away some
of the error that mymethod of using a string created.
After I had the measurements I layed them out in a table. The objects that
I measured were a small flask, a large flask, a tray from a scale, a roll of tape,
a roll of paper towels, and a spraycan.
By dividing the circumference of the circle by the diameter I was able to
calculate the experimental ratio, and I knew that the accepted ratio was pi. Then
I put both ratios in the chart.
By subtracting the accepted ratio from the experimental you find the error.
Error is the deviation of the experimental ratio from the accepted ratio. After I
had the error I could go on to find the percentage error. The equation I used was,
error divided by the accepted ratio times 100. For example, if I took the error of
the experimental ratio for the paper towels, which was 0.12. I took that and
divided it by the accepted ratio giving me .03821651. Then I multiplied that by
100 giving me about 3.14. Using these steps I found the percentage error for all
of the objects measured.
The next step was to graph the results. I was able to do this very easily
with spreadsheet. I typed in all of my data and the computer gave me a nice
scatter block graph. I also made a graph by hand. I set up the scale by taking
the number of blocks up the side of my graph and dividing them by the number
of blocks across. I placed my points on my hand drawn graph. Once I did this
I drew a line of best representation because some of the points were off a little
bit due to error.

By looking at my graph I can tell that these numbers are directly
proportional to each other. In this lab it was a good way to learn about error
which is involved in such things as measurements, and also provided me with
a good reminder on how to construct graphs.
There were many errors in this lab. First off errors can be found in the
elasticity of the string or measuring tape. Second there are errors in the
measurements for everyone. Errors may be present when a person moves
their finger off of the marked spot on the measuring device.


Object Circumference Diameter
small flask 20.5 6.3
large flask 41.3 12.9
tray from a scale 40.1 9.5
roll of tape 6.4 1.2
roll of paper towels 44.5 11.8
spraycan 25.1 7.7