Shafted

dudeney drilled ball puzzle

From Henry Dudeney:

A ball 13 inches in diameter has a hole 5 inches wide drilled through the center. How deep is the hole?

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Pythagoras solves this neatly: x² + 25 = 169; x = 12. Curious addendum: If you now hold the hole’s depth constant at 12 and vary its width, adjusting the object’s diameter accordingly, the object’s volume remains constant. (Thanks, Thomas.)