20-CS-110-001 |
Introduction to Computer Science |
Fall 2010 |
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**Solution to Hole in Sphere Puzzle**

_----_ <- height of piece showing at top = (r-x/2) / | | \ |\ | | | | | x/2| \r | <- the hole | |x | | | \ | \ | | / |___\___| -____- ^ ^ | |-- center of sphere |---- sqrt(r^2 - x^2/4)Volume of hole: π*( r^{2}-x^{2}/4)*x + ...Volume of sphere: 4*π* r^{3}/3
Volume of piece of sphere: int{t=x/2,r} π*
whole sphere:
end pieces:
2*π*(
hence, hole volume =
Remaining volume =
If the radius of the hole is |