### Brain Teasers

# Soda Bottle

You have a typical soda bottle, which is designed such that the bottom 3/4 is a perfect cylinder and the top 1/4 is an irregular shape. The bottle is filled about half way with soda. Using only a ruler, how can you determine exactly what percentage of the bottle's volume is filled?

### Answer

First measure the height of the liquid in the bottle with the bottle upright. Then, turn the bottle upside-down and measure the amount of space: the distance from the top of the liquid to the bottom of the bottle.You have now found the heights of liquid and air in terms of the cylinder only. You have essentially taken the irregular shape out of the equation. Simply divide the height of the liquid by the sum of the two heights to get the volume percent of the liquid in the bottle.

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