Find Depth of Water in a Tank
Date: 08/02/2003 at 04:16:59 From: Hasan Subject: Volume A rectangular tank measures 4m long, 2m wide and 4.8m high. Initially it is half full of water. Find the depth of water in the tank after 4000 litres of water have been added to it.
Date: 08/02/2003 at 22:18:36 From: Doctor Ian Subject: Re: Volume Hi Hasan, Try thinking of it this way. Imagine there are two tanks instead of one. They're the same size, but one is full, and the other is empty. What size are they? They're each half as tall as the single tank in your problem, so the dimensions are length = 4 m width = 2 m height = 2.4 m Here's a picture of the situation: Old problem +---------------+ 2m / /| / / | +---------------+ | 4.8 m | | | | | | | | + | | / | |/ +---------------+ 4m New problem +---------------+ 2m / /| 2.4m / / | +---------------+ + | | /| 2.4m | |/ | +---------------+ + | | / | |/ +---------------+ 4m So now we want to know: If we put 4000 liters of water into the top tank, how high will the water level be? And when we figure that out, we can add 2.4 meters to it to get the answer to _your_ problem. Does this make sense? Okay, so how do we get the height of the water in the top tank? Well, we can change the problem a little bit again. What if we have a tank that holds exactly 4000 liters of water? If the length is 4 meters, and the width is 2 meters, how high will that tank be? The volume of a rectangular prism (which is the name of this kind of shape) is volume = length * width * height We know the volume: It's 4000 liters. And we know the length and width. So 4000 liters = 4 meters * 2 meters * ? meters But there's a problem! On the right, we get a volume of (4 * 2 * ?) cubic meters while on the left, we have the same volume expressed in liters. What you'll want to do is find out how many liters are in a cubic meter, and convert: 1 cubic meter 4000 liters * ------------- = 4 meters * 2 meters * ? meters ?? liters And then you just have to figure out what value of '?' makes the equation true. When you have that, you know the height of a tank that would hold exactly 4,000 liters. That's the same as the height of the water level in the top tank, and if you add 2.4 meters to that, you get the water level in the original tank. Were you able to follow all this? It illustrates an important point, which is that most of the time, when you're solving a math problem, what you're looking for isn't an immediate answer, or a formula that can get you the answer in one step. What you're looking for is a way to change the problem you have into one that would be simpler to solve. In this case, we did that twice. First, we didn't want to worry about the water that was already there, so we pretended it was in a separate tank. Then, we didn't want to worry about water level separately from the volume of the tank, so we tried to find the volume of a tank that could hold _only_ 4000 liters of water. Does this help? Write back if you'd like to talk more about this, or anything else. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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