Math CentralQuandaries & Queries


Question from Eddy:

we have a washing machine with a specific cylinder size, which we could calculate the volume as a regular cylinder formulas. The question is, if we fill the washer cylinder with water at a specific height on water , example 15 cm height, how can we find the volume of water at that specific height?

Hi Eddy,

Stephen answered this question a while ago for Andy who had a cylinder of radius 5 feet and a length of 35 feet. If you follow through his argument you can develop a general expression.

Suppose the cylinder has radius r cm, length h cm and you fill it to a depth of d cm. The volume of water in the tank is the area of the end (the blue region in Stephen's diagram) times the height h. Following Stephen's development the area of the end is

areasquare centimeters

and hence the volume of water in the tank is

volumecubic centimeters.

Remember to set your calculator for radians (not degrees) when using this equation or you'll get nonsense answers.

I hope this helps,

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