Math CentralQuandaries & Queries


Question from RAY:

How can I determine the exact amount of liquid in an overturned drum?


We have two responses for you


If the drum is roughly a cylinder, then the water also forms a cylinder with smaller height.
The formula for the volume of a cylinder is pi * r2 * h. Pi is about 3.14159, r is the radius
if the cylinder (distance from the center of the drum to the start of the outside edge, and h
is the height (of the water). If your measurements are in inches (say), then the result will
be in cubic inches. According to Wikipedia:

1 US Gallon (liquid) = 231 cubic inches
1 UK Gallon = 277.4 cubic inches

If your measurements are metric it is easy: there are 1000 cubic centimetres in a litre.




Victoria's response assumes the drum is standing on its circular end. If the drum is lying on its side then the expression is a little more complicated.


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