PI (n) is the ratio of the circumference of a circle to its diameter. The value of this ratio is constant regardless of the size of the circle; thus pi is a universal physical constant. The diameter and circumference of several circles were measured by CHEM 1114 students, each using a different ruler. (Include units below if applicable. If necessary, use a separate sheet of paper for 6c and 7c.) 1. Inspect the data below and calculate the value of pi using two pairs of the data: 2. Prepare a hand-drawn plot of the two variables on the reverse side of this worksheet. Include a title, axis labels (with units), and a trendline. Estimate the circumference of a circle with a diameter of 4.50 cm: Estimate the diameter of a circle with a circumference of 3.94 inches 3. a. Prepare a plot using graphing software. Include a title, axis labels (with units), the equation of the best-fit line and the R value on the graph. b. Re-write the equation of the best-fit line substituting "Diameter" for x and "Circumference" for y directly on the graph. C. Attach the fully labeled graph to this worksheet. 4. What is the value of pl based on the equation for the best-fit line? 5. Determine the percent error using the definition of percent error: Use a value of 3.142 for the actual value of pl. Actual-Experimental Actual % error= x 100 s Eror - 6. Using your computer-generated graph, a. visally estimate the circumference of a circle when the diameter is 4.50 cm: , b. calculate the circumference ford-4.50 cm using the equation of the best fit line: Use the graph to ensure that this value is reasonable. c compare the calculated circumference to the two visually Interpolated values (Steps 2 and 6a). Briefly discuss any discrepancies. 7. Using your computer-generated graph, a. visually estimate the diameter of a circle with a circumference of 3.94 inches: b. calculate the diameter using the equation of the line: Use the graph to ensure that this value is reasonable. c. compare the calculated diameter to the two visually interpolated values (Steps 2 and 7a). Briefly discuss any discrepancies. Data: Circumference (y) TT Diameter (x) 1.38 cm 4.08 cm 3.80 cm 4.70 in 1.56 in 12.5 cm 2.06 in 6.43 in 7.28 cm 8.57 in