At Gathering 4 Gardner, Colm Mulcahy suggested I try the following 3D-printing project.
Recall the "napkin ring problem": Take a sphere of radius r and drill out a hole along a diameter so the remaining shape has height h. Then the volume, V = πh³/6, does not depend on r.
He thought that if we print these shapes as solids (i.e., with 100% fill), they should all weigh the same. See the following post for the results.
Recall the "napkin ring problem": Take a sphere of radius r and drill a hole along a diameter so the resulting shape has height h. Then the volume, V = πh³/6, does not depend on r!These files consist of drilled spheres of the type described in the problem. Each has a height of 4cm, but the radii are 4.15 cm, 5 cm, 7 cm, and 10 cm. It is essential that you print them with 100% fill. If you do, you will find that they all weigh the same amount and hence have the same volume.Thank you to Colm Mulcahy for suggesting this project.
Sryvk
Dave Richeson
Karen Campe