Determining the Ratio of Circumference to Diameter of a Circle
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 laid 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.
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 laid 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.