Volume of a bead

[Albert Chan]

Find a gem of science/math stuff link: https://www.lockhaven.edu/~dsimanek/home.htm

Physics Q&A: https://www.lockhaven.edu/~dsimanek/puzz...nswers.htm

#1 Normally, a bridge is build on top of river, with ships passing beneath it.
-> But there is water bridge, with ships run on top of it ...

#66 holey sphere, about volume of bead. Solution by Martin Gardner ...

---

I were trying to get a volume of bead with square hole (side 2 r).
Its volume must be less than bead with round-hole, radius r.

My first approximation for removed square holes volume
~ 4/Pi * volume of removed sphere round-hole
= 4/Pi * (4/3 * Pi * (R^3 - h^3))
= 16/3 (R^3 - h^3), where h = sqrt(R^2 - r^2)

Volume of square-holed bead ~ 4/3 Pi R^3 - 16/3 (R^3 - h^3)

For relative small r, is that close ?