Mastodawn

Another 3D-printing suggestion from Colm Mulcahy:

Archimedes proved that if you slice a sphere of radius r with two planes a distance h apart, the surface area is 2πrh—the same as a cylinder of the same radius and height. So, it doesn't depend on where the slicing occurs.
1/2

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Dave Richeson Feb 28

Idea: Produce 3D-printed slices of a (hollow) sphere, all of the same height. Print with 100% fill. They should all weigh the same.

Bam!

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Sibrosan Feb 28

@divbyzero

I propose you try it with a hollow sphere of 30.0 cm diameter and a shell thickness of 14.9 mm, printing slices of 1mm thickness, one taken near the middle, and one just at the top of the sphere.

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Dave Richeson Feb 28

@sibrosan Did you see the second of the two posts? That's essentially what I did (but with different dimensions).

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Sibrosan Feb 28

@divbyzero

If you did it with the dimensions I suggested, you would find that the slice from the middle weighed much more than the slice from the top.

In your case (with a much thinner shell) the difference might be small enough to dismiss as measurement error, but if accurately printed and weighed it will be there.

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Dave Richeson

@sibrosan Ah! I misuderstood your original comment. I thought you just wanted me to make the model larger. You are 100% correct. In fact, this is version 2.0. For version 1.0, the sphere was smaller with the same thickness walls, and when I sliced the sphere straight across, the difference in weight was measurable. So, in this version 2.0, I made the sphere larger and the slices are sliced along cones converging at the origin rather than along flat planes. That way, the "height" of each radial shell in the thin solid object is the same. (It has the added benefit that one ring sits slightly inside its neighbor, which is nice.)