Math CentralQuandaries & Queries


Question from Alexander:

if a cylindrical water tank has diameter of 90cm and leak starts at the bottom 10 litres in an hour. how long will it take for the level to fall by 20cm

Hi Alexander,

The volume of a cylinder cylinder is $\pi \; r^2 h$ where $r$ is the radius and $h$ is the height. Thus the volume of water that is lost through the leak is

\[\pi \; \left(\frac{90}{2}\right)^2 \times 20 \mbox{ cubic centimeters.}\]

There are 1000 cubic centimeters in a litre so how many litres is that? At 10 liters per hour how long will it take to lose that much water?


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