[Class discussion of soap box volume and surface area. Use alphabet blocks.]
Volume and surface area of a sphere with a radius r. Note that the radius r is equal to half the diameter.
Uncertainty: the limit of our measuring tools for a single measurement, our uncertainty based on the smallest measurement our tools can accurately make. For a ruler marked in millimeters there is always at least a half a millimeter of uncertainty, often more.
Precision: the average variation in multiple measurements of an experiment usually expressed using the standard deviation
Error: the difference between the measured result and the actual value. The actual value is always unknown, hence the error is never truly known.
[Ensure agreement on length, width, and height dimensions for box of soap]
Given that there is uncertainty in any measurement, how can we report derived calculations such as volume or surface so as to improve the precision (make the standard deviation smaller) of our results?
Multiple teams taking multiple measurements provides a series of checks on each other in our work. Then the tools of statistics can be used to best report the volume and surface area. The mean will capture the best estimate of the volume and surface area. The standard deviation will capture the best estimate of uncertainty in our estimate.
Measurements of the volume and surface area of boxes and spheres will be conducted by the class using rulers. Each team will measure their own soap boxes and then report their results to tables on the board.
Box of soap
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Brand |
Length/cm |
Width/cm |
Height/cm |
Volume/cm³ |
Surface area/cm² |
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Super ball sphere
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Diameter/cm |
Radius/cm |
Volume/cm³ |
Surface area/cm² |
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Volume box of soap /cm³ |
Surface area box of soap/cm² |
Volume box of soap/cm³ |
Surface area box of soap/cm² |
Volume super ball sphere/cm³ |
Surface area super ball sphere/cm² |
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Data Analysis and Results[In class presentation on calculator usage] |
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Volume box of soap /cm³ |
Surface area box of soap/cm² |
Volume box of soap/cm³ |
Surface area box of soap/cm² |
Volume super ball sphere/cm³ |
Surface area super ball sphere/cm² |
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Mean (average) |
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Standard deviation |
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[No graphs required in this laboratory]
Discuss how the teams provided checks and balances on each other's data. Discuss your own thinking on the best way for student teams to generate reproducible, repeatable volume and surface area results. Discuss any problems your team faced in the laboratory.
Use a spreadsheet and/or word processing package to type up a report using the sections seen above. Include your tables. [MAYBE PULL THIS LAB VISIT AND RUN WITH THE CALCULATOR APPROACH TO STDEV] The class will spend the final portion of the period in A204 to learn how to do this. Lab reports are due a week later at the next laboratory period. The lab report can either be a hard copy from a printer or emailed to dleeling@comfsm.fm Put your name on the report! Is soap sold by volume? [Cover save as... in A204]