Archimedes Principle

youmagine

This is part of a series of 30 exercises developed during the E3D+VET program. The aim of this Erasmus+ program is to fully immerse VET centers in 3D printing (website: https://www.e3dplusvet.eu/). The plan is to print pieces with various basic geometries, such as cylinders, spheres, cubes, pyramids, and so on. Students will have to calculate the volume of these pieces and then submerge them in a measuring cylinder filled with water. They will need to check how much water the piece displaces and verify that it's exactly the same as the volume of the piece. It's recommended to print the pieces at 100% infill, so they're completely submerged in the water. Example: Printing a cube: Cube volume: a^3 = 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 this diameter is 3 cm. If students submerge the cube inside the measuring cylinder filled with water, they'll be able to see that the displaced height is approximately 1.15cm. So, they'll have to check that the displaced volume equals the volume of the cube: Pi*R^2*Δh = a^3 -> 3.14*1.52*1.15 = 8.1 ≈ 8 Volumes: 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