Post #2712459
2026-02-28 22:35 UTC
@sibrosan@mastodon.social @divbyzero@mathstodon.xyz
Well, I'm not a mathematician, but I can prove it. I don't know into how much detail a proof must go to convince you, but here is an attempt:
We have a shell delimited by an outer sphere with radius R and an inner sphere with radius r. The spheres have the same center C.
(In your example R = 150 mm and r = 1 mm, but we need not restrict ourselves to these values.)
1. Select some piece P of the outer sphere.
Replies (1)
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@hcschuetz@mastodon.social 2026-02-28 22:36
@sibrosan@mastodon.social @divbyzero@mathstodon.xyz 2. Construct a solid S consisting of all the points between C and some point of P. We get: volume(S) := area(P) * R / 3. 3. Construct another solid s by contracting S towards C by the factor r/R. We get: volume(s) = (r/R)^3 * volume(S)