Solution
The whiskey bottle problem was not difficult. I received several solutions, but one stands out — that by Ken Duisenberg:
If 3 cm of whiskey are removed, the bottle would be half full.
When right side up, the whiskey level goes to 14 − 3 = 11 cm.
When upside down, whiskey goes to 19 − 3 = 16 cm, leaving 11 cm of air at the top of the upside-down bottle.
So there is the same amount of whiskey and air in the bottle. Therefore, the total amount of whiskey is
(1/2)750 + [3π(3.5²)] = 490.454 ccs.
By the way, Bob would have drunk 260 ccs of whiskey in a day — rather a lot.
[Back to Problem 1191]
© Copyright 2014 Stan Wagon. Reproduced with permission.