Post #2712460
2026-02-28 22:36 UTC
@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)
Replies (1)
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@hcschuetz@mastodon.social 2026-02-28 22:37
@sibrosan@mastodon.social @divbyzero@mathstodon.xyz 4. Notice that s is contained in S. If we remove s from S, the remaining solid is the part of the shell between P and the corresponding piece of the inner sphere. It has the volume volume(S) - volume(s) = volume(S) * (1 - (r/R)^3) = area(P) * R / 3 * (1 - (r/R)^3)