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Problem of the Week 1191

The Whiskey Bottle

Alice: Have you been hitting the bottle again? Yesterday this bottle of whiskey was full, but today there are only 14 centimeters of whiskey in it.

Bob (turning the bottle upside down): Fourteen? Look: There are still 19 cm of whiskey in the bottle.

Given that a full bottle holds 750 cubic centimeters (cc), the bottle is 27 centimeters from top to bottom, and forms a cylinder of diameter 7 centimeters, except for the bottom (which has a small indentation) and the stem (which is a small, narrow stem typical of whiskey bottles), as in the figure to the right.

How much whiskey is in the bottle, in cc?

Source: I believe this problem is due to Robin Hartshorne.

© Copyright 2014 Stan Wagon. Reproduced with permission.

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24 September 2014