Determining The Ratio Of Circumference To Diameter

Of A Circle Essay, Research Paper

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