Equal Volume Solids Set + MakerEd Project

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This equal volume solids set is used to explain why bubbles are round. Spherical, to be exact. The sphere is the shape that uses the smallest surface area to enclose the largest volume! The set includes five solids: sphere, cube, pyramid, cylinder, and torus. Each has a volume of 125 cm3, and the surface areas range from 121 cm2 (sphere) to 168 cm2 (pyramid). There are two Projects recommended with this set. One is to challenge students to make a bubble in another shape, using a frame or other method. Another is to challenge students to design another shape with the same volume as the set, using their knowledge of geometry and the 3D design program of their choice, and then to find its surface area. MakerEdProject Print Settings Printer Brand: MakerBot Printer: MakerBot Replicator 2 Rafts: Doesn't Matter Supports: No Resolution: 0.2mm Infill: 5-10% Notes: These are uncomplicated models to print. Each is situated to provide the best resolution on the letters. Rafts are optional. Supports may interfere with the letters. How I Designed This Calculations I used readily available geometry formulas to find the dimensions of various solid shapes with volume of 125cm3. Then I used those dimensions to find the surface area of each solid. Design Shapes were designed using Tinkercad. I created blocks of lettering that were angled or curved to match the surfaces of the shapes. Project Idea One - Bubble Challenge Objective Create a soap bubble with a shape other than a sphere (or near-sphere). Audience Kids or adults age 5 and up. Preparation Print the Equal Volume Solids Set. Prepare or purchase bubble solution. (I like the Guar Gum recipe at http://soapbubble.wikia.com/wiki/Recipes_Guar#Recipes , but any will work.) Find or make some ordinary bubble wands. Clothesline wire or coat hangers work well. Make some wands in different shapes (square, triangle). Add some materials - string, straws, pipe cleaners, more wire, for making custom wands and frames. Steps Blow bubbles with a round wand. The bubbles are round(ish). Blow bubbles with different shaped wands. Are the bubbles different shapes? Probably not. Examine the Equal Volume Solids Set. Note that the sphere encloses the volume with the smallest possible surface area. Explain that bubbles are round for this reason. The bubble film has to stretch the least and can enclose a large volume of air. Challenge students to make a bubble in a different shape. Frames that hold the bubble in place are allowed. Results Invite students to share their bubble frames or wands, and demonstrate how they work. Project Idea Two - Design a Solid Objective Practice precise 3D Design and geometry skills by creating a solid shape with a specific volume, and calculating its surface area. Audience Beginning 3D designers approximately age 13 and up, especially geometry students. Preparation Print the Equal Volume Solids Set. Find a reference list of formulas for volume and surface area of solids. Introduce students to basics of 3D design, if this is completely new to them, using whatever program you want them to practice. Steps Show the Equal Volume Solids Set, and let students deduce the patterns of volume and surface area for the different shapes. Challenge students to design a shape that has the same volume (125cm3), but is not one of the shapes in the set. For advanced students, suggest grouping two or more shapes together to achieve the target volume. Print or view student designs. Results Let students share their work. Volume could be tested using displacement of water, if an objective assessment is desired.