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Secondly, your method is quite involved and will disturb the very system you're trying to observe. You would find the volume of the water by filling the container with water. So, if you had that specific amount of water in the barrel for a reason, you've just that up by filling the barrel. Besides, filling a tank with a measured amount of fluid is a lot of work. Isn't it simpler to just figure out the volume as a function of fluid depth?
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The purpose of most tanks is to hold fluid obviously. If they didn't need this water for some reason then why have the tank?Obviously if they can't or don't want to add water to it then they shouldn't. But if their goal is simply to figure out how much water the tank holds AND they plan on filling it anyway then it's a perfectly acceptable approach. Rather than criticize others for their answers, how about accepting that there are other paths that can be taken besides the formulaic approach?
You seem to be taking this question far too personally.