E3D+VET exercise: Archimedes Principle

thingiverse

This is part of a series of 30 exercises developed during the E3D+VET program, an Erasmus+ initiative aimed at immersing VET centers in 3D printing. The website for this program is https://www.e3dplusvet.eu/. The idea behind these exercises is to print pieces with different basic geometries, such as cylinders, spheres, cubes, pyramids, and more. Students will have to calculate the volume of each piece and then submerge it in a measuring cylinder filled with water. They'll need to verify that the amount of water displaced by the piece matches its calculated volume. To achieve accurate results, it's recommended to print the pieces with 100% infill so they fully immerse in the water. Example: Printing a Cube Cube Volume: a·a·a = 2cm·2cm·2cm = 8cm^3 Displaced Volume in the Measuring Cylinder: First, students will need to measure the internal diameter of the measuring cylinder. Let's say it's 3 cm. When they submerge the cube inside the measuring cylinder filled with water, they'll see that the displaced height is approximately 1.15 cm. Now, they'll have to check that the displaced volume equals the cube's volume: Pi·R^2·Δh = a·a·a -> 3.14·1.52·1.15 = 8.1 ≈ 8 Volumes of Various Shapes: Cube: a^3 Cylinder: pi·r^2·h Pyramid: (1/3)·a^2·h Sphere: (4/3)·pi·r^3 Torus: (1/4)·pi^2·D·d^2