Circumference and Diameter Printer Friendly Version
Purpose

To let each student become familiar with measuring with meter sticks and to develop critical thinking skills. Secondly, to introduce students to data analysis techniques.

Vocabulary

Match the correct definition to each term.
 1. accuracy

 2. centi

 3. circumference

 4. deci

 5. dependent variable

 6. diameter

 7. independent variable

 8. kilo

 9. meter

 10. micro

 11. Mega

 12. milli

 13. parallax

 14. precision

 A metric prefix representing 0.1 of a quantity A metric prefix representing 0.01 of a quantity A metric prefix representing 0.001 of a quantity A metric prefix representing 0.000001 times a quantity A metric prefix representing 1000 times a quantity A metric prefix representing 1000000 times a quantity A measure of the closeness of an experimental measurement with an accepted standard. The apparent shift in an object's position when it is viewed from an angle. A measure of how well an outcome can be reproduced one trial after another. The length of a circular object's perimeter. The length of the longest chord in a circle. The distance that light can travel through a vacuum in 1/299792458 seconds. The values for this experimental quantity are plotted along the y-axis. The values for this experimental quantity are plotted along the x-axis.
Metric Conversions

Using decimal representations (not scientific notation), supply the correct conversions for each row in the table.

 cm µm km
 1 decimeter
 1 millimeter
 1 megameter

Record the values for each specified position to the nearest hundredth of a centimeter. Please do NOT include "cm" on each answer - just input the numerical value.

 A

 B

 C

 D

 E

 F

Measuring diameter and circumference.

Measure, do NOT calculate, the diameter AND circumference of each item listed. Each member of the lab group is to do his/her own independent measurement. On a sheet of notebook paper, record all measurements and then calculate an average value for each set. You and your partner need to be consistent with your measurements so that you always have the same number of decimal places on all values.

 Description Diameter Circumference Partner 1 Partner 2 Average Partner 1 Partner 2 Average pen case washer soda can inside of tape coffee can top of plate bicycle wheel

Graphical Analysis

EXCEL will now graph your data. Minimize your browser, double click My Computer, double click the shared drive on Lederman, double click your period's folder and then finally double click 1-circumference.xls. You will most likely be asked to open the file as "read only" - that is fine. As soon as the file is open, use File Save As to rename the file as

LastnameLastnameCircumference.xls

in your period's folder. This copy of the file now belongs uniquely to your group. Remember that there are to be no spaces in the file name.

Input your final AVERAGE values for Diameter and Circumference. Diameter, measured in cm; will be placed on the x-axis and Circumference, measured in cm, will be placed on the y-axis. As you enter your data, your graph will grow. When the graph is finished, be certain to investigate any points that are obviously out-of-line. Recheck them for accuracy - initially as a error in typing; otherwise go back and re-measure. When you data fits nicely, resave and print your graph from my teacher station. Student stations do not have permissions to print to a local or network printer.

Error Analysis

The value for the slope should be close to π (π =3.14159265). Calculate the accuracy of your experimental measurements by finding the percentage error for your experiment. This done by using the following formula

and should be shown on your graph's printout. On your graph, do not just give me the final numerical value, show me your calculation.

Since this graph is linear, we have discovered that the circumference and the diameter of circular objects are directly proportional. Their proportionality constant [that is, their slope] should have been pi. Ideally, your y-axis intercept should have been ZERO.

Also on your graph, write the equation of your line next to your line. Remember to not use the variables "x" and "y" but the correct variables that correspond to our experimental values, circumference and diameter. The values for the slope and y-axis intercept for your regression line are already displayed on the graph.

Let's look at an example. If your slope was 3.24 and your y-intercept was -0.75, then your equation would be:

C = 3.24 D - 0.75

 Using your equation, extrapolate the circumference of a circular conference table that has a diameter of 91.4 cm.

Lab Report.

After you finish submiting this page turn in your lab reports to the one-way box: title page, handwritten summary data chart, and your annotated graph.