Determination of Pi

Purpose

Pi is a constant that we have used many times. In this activity, you will be determining the value for this constant by measuring a variety of circular lids.

Background

The circumference of a circle gets larger as the diameter increases. If we look at that ratio, we can see that it is equivalent to pi. Anytime we are looking at a ratio, you should think about slopes. A slope is a ratio of the rise over the run and we can make this if we collect data of the circumference (rise) over the diameter (run). By graphing our data, we can use a line of best fit to determine the value of pi.

Materials and Procedure

Items needed for lab:

• A set of 4-5 lids of various diameters
• A metric ruler
• A piece of string

1. Use the ruler to find the diameter of a lid. Be sure to read it to the correct significant figures. Record this as your x value for the graph.
2. Wrap the string around the lid. Use the ruler to find the circumference. Be sure to read it to the correct significant figures. Record this as your y value for the graph.
3. Repeat 1-2 for all of the lids.

Calculations

You will be using a spreadsheet to create the graph and determine the slope of the line of best fit. Follow along with the group as we use the spreadsheet.

Analysis and Discussion

Pi is a known value. Find the percentage error for your slope from the actual value. Because pi is irrational, you will only need to use the number of digits that matches your experimental precision.

Use the following questions for discussion:

• Why can’t you report an experimental value for pi to 10 digits?
• What lid seemed to fit the line of best fit the best?
• How did your group compare with other groups?
• What seems to be a level of acceptable error for this lab?