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Name: TA NamerLab Section: Pi (tt) 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 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 pi 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 pi. % error = Actual - Experimental Actual x 100 Error- C. 6. Using your computer-generated graph, a. visually estimate the circumference of a circle when the diameter is 4.50 cm: b. calculate the circumference for d = 4.50 cm using the equation of the best fit line: Use the graph to ensure that this value is reasonable. 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 link 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: Diameter (x) Circumference tyl 1.38 cm 4.08 cm 4.70 in 12.5 cm 3.80 cm 1.56 in 2.06 in 7.28 cm 6.43 in 8.57 in