The Billiard Ball
The world-famous pool player, "Skinny Dakota" is over at your house demonstrating trick shots. After showing off some of his trademark moves, including the "Rail Escape," "Around the World," and "Bubble sorting the rack", he demonstrates his most impressive shot. In a staggering display of skill, strength, and total lack of concern for other people's property, he has blasted a perfectly cylindrical hole straight through the center of the cue ball.
"Do you know," he says, "it is possible to figure out the volume of the remainder of the cue ball, knowing only the length of the hole?"
"Impossible," you reply, "this isn't a regulation cue ball."
"No problem, watch."
He produces a tape measure and hands it to you, saying, "Measure the distance between the opening on one side and the other, but don't measure the diameter of the ball or the radius of the hole."
You do as he says and report, "Exactly two inches."
"From this information, you can deduce the remaining volume of the ball. In fact, I'll make a wager- if you can figure it out or I'm lying and it can't be solved with the information given, I'll buy you an entire set of new balls. If you can't figure it out and it can be done, you owe me a new cue stick. Naturally I'm assuming you know the rudiments of geometry and the formulae for the volumes of simple solids."
"Naturally," you answer, "I'll take that wager. It sounds like I can't lose."