This is part of the series of 30 exercises developed during the E3D+VET program. The aim of this Erasmus+ program is the immersion in 3D printing of VET centres (website: https://www.e3dplusvet.eu/).

The idea is to print pieces with different basic geometries, such as cylinders, spheres, cubes, pyramids, etc. Students will have to calculate the volume of these pieces and then immerse them in a measuring cylinder filled with water. They will have to check how much water the piece is displacing and verify that is the same as the volume of the piece.

It is advisable to print the pieces with 100% of infill, so that they are completely immerse in the water.

Example printing a cube:

Cube volume: a·a·a = 2cm·2cm·2cm = 8cm3

Displaced volume in the measuring cylinder:
First of all, students will have to measure the internal diameter of the measuring cylinder. Let say this diameter is 3 cm.
If students immerse the cube inside the measuring cylinder filled with water, they will able to see that the displaced height is approximately 1.15cm.
So, they will have to check that the displaced volume is equal to the volume of the cube:

Pi·R^2·Δh = a·a·a -> 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