Transcript Learning About Related Rates AP Calculus AB Mrs. Kamkutis Using a blow-pop to discover the rate of change of volume. Adapted from a lab project.

Learning About Related Rates
AP Calculus AB
Mrs. Kamkutis
Using a blow-pop to discover
the rate of change of volume.
Adapted from a lab project by Nancy McKinney, Camdenton High School
Table of Contents
 Lab Description
 Procedure
 Calculations
 Lab Report
Lab Description
• Materials Needed: rulers (in millimeters), heavy string, stopwatches
or clocks/watches with second hands, Blowpops (only one Blowpop
is recorded per pair of students for the actual experiment, but BOTH
students will want one!)
• Objective: The student will determine the rate of change of volume
of a sphere using experimental data.
• Task: Working with a partner, the students will collect data, perform
calculations, and form conclusions which will be detailed in a written
or oral lab report.
• Time Allowance: The experiment can easily be finished in a 50minute class period, but more time will need to be needed to
prepare the lab report.
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Procedure
a)
b)
c)
d)
Working with a partner, determine
the initial radius of the sucker
(assume it is a perfect sphere).
Place the sucker in your mouth and
consume carefully and constantly
for one minute.
Measure the radius again and
record it in a neat and organized
format.
Repeat steps b) and c) until you
have reached the bubblegum
center.
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Calculations


From your data, determine the
rate of change of the radius of
the sucker. This may not be a
constant rate, so estimate the
average rate over the time
period.
Using the rate from the previous
step, set up an equation to
calculate how fast the volume of
the sucker is decreasing. Use
derivatives to calculate the rate
when the radius is three-fourths
its original value.
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Lab Report
Write a concise and organized lab report
that contains the following elements:



A brief description of the process and
statement of purpose
All calculations used
A conclusion including all findings
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