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

Category: Science