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 50-minute class period, but more time will need to be needed to prepare the lab report. Back to Table of Contents

Procedure 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. Back to Table of Contents

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. Back to Table of Contents

Lab Report A brief description of the process and statement of purpose 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 Back to Table of Contents