Calculus Project 4: Using submersion to find volume

thingiverse

This is the fourth part of a series of projects intended for first year calculus students. In this series, students will learn how to use different mathematical equations to assess the properties of solids and containers. In this part we will be using the castes made from part 3 to check the work we accomplished in part 1. Part1:http://www.thingiverse.com/thing:1368258 Part 3:http://www.thingiverse.com/thing:1373188 Print Settings Printer: CraftBot Rafts: No Supports: No Resolution: optimum Infill: 30% square Notes: I optimized this thing to be printed in ABS with maximum settings. I would recommend a skirt with an offset of 0mm (otherwise known as a brim) with 2-5 loops for ABS. I would also suggest an increased infill ratio. How I Designed This For this project I used a free program from Autodesk called TinkerCAD. I have long been a user of AutoCAD which is a desktop drafting program from the same company. I used TinkerCAD to make it easier for educators and learners to be able to more easily replicate what I did. TinkerCAD is awesome because it's not only free, but it's easy to use. It also runs in your browser and has built in instructional lessons. www.tinkercad.com For part 4 of this project I started out with our product from the part 2. If you remember, we used X=20mm which gave us a base of 60x20mm, two flaps with dimensions of 60x20mm, and two flaps with dimensions of 20x20mm. We then made this into a mold by adding a channel around the base and extending the flaps. Part 2:http://www.thingiverse.com/thing:1371700 Project: Using submersion to find volume Objective At the end of this part of the project students will be able to test/prove the math that they used in part 1 of this project. Audience Even though the overall project is designed for Calculus students, this part of the project can be used for algebra students as well. Preparation Teachers will need to make sure they have access to graduated cylinders with mL/MM3 markings. Teachers will have needed to complete all other steps of this project already, preferably with their class Step 1: Setup graduated cylinders Place graduated cylinders on a table visible to all students. Add just enough water so the castes from part 3 can be submersed. Step 2: Record water level Make sure you record where the water level is BEFORE you submerse any castes, and in-between submersing each one. Step 3: Submerse castes Submerse the castes that you created in part 3, one at a time. Step 4: Calculate volume To find V, you must take the water level before submersion, and subtract it from the water level after submersion. Step 5: Compare Compare the volumes that you recorded from this part to the numbers that you calculated from part 1. If all goes well, your numbers should match up pretty well. Results Students now have gone from creating a lidless box, to calculating it's formula, and now even to proofing that their formula works. Now they are ready for part 5; charting their data!