The mysterious drilled sphere
A drill bit of unknown diameter perforates a sphere of unknown volume, accurately passing through its center. The cylindrical hole is measured to be 6 inches long. What is the remaining volume of the sphere to 3 decimals accuracy? Any idea of its diameter in inches? (use pi=3.14159
)
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1 solution
The sphere could be the size of Uranus, no pun intended, in which case the drill bit would be colossal, yet the hole still a measly 6 inch in length, the remaining volume equal to that of a sphere of 6 inches in diameter with an infinitely tiny (and breakable!) drill bit. The thickness of that band of material running around the planet would be an atom in thickness or less, I suppose. That proof can be performed on just 2-3 tryouts...or smarter men than myself could develop a math proof, in which case I would be grateful to see it here. Someone to verify my assumption of the one-atom thickness of the Uranus band would be even more exciting. Thanks to all.